en. Thus,Range ∈ [1 2 2 − 1, 1] = [1 2, 1] Was this answer helpful? 0. We know that a function f x is increasing then f ' x > 0. Matrix. Thus,Range ∈ [1 2 2 − 1, 1] = [1 2, 1] Was this answer helpful? 0.Q . Period of sin4x = π. Best answer. Total number of solution (s) of the equation sin4x+cos4x =2 in [−2π,2π] is : View Solution. The expression in bold is the Pythagorean Identity for trig functions: it is equal …
How to simplify \sin^{2}{x} +\cos^{4}{x}-\sin^{4}{x} +-cos-4-x-sin-4-x my favourite way: I would just repeatedly use the …
How do you use the power reducing formulas to rewrite the expression sin4xcos4x in terms of the first power of cosine? 1281 (3−4cos(2x)+cos(4x)) Explanation: Use sin2A = …
First you multiplied by \sin{4x}. Q 3.
hint: $\sin^2 x + \cos^2 x = 1$; if you square that, you get $$ \sin^4 x + 2\sin^2 x \cos^2 x + \cos^4 x = 1, $$ which you can turn into $$ \sin^4 x + \cos^4 x = 1 - 2\sin^2 x \cos^2 x $$ and that lets you get rid of the 4th powers in the left hand side.
simplify \frac{\sin^4(x)-\cos^4(x)}{\sin^2(x)-\cos^2(x)} en. A. $\endgroup$
Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step
Multiply (1) ( 1) by tan4 x tan4 x tan 4 x tan 4 x we obtain. One more thing, I don't feel comfortable with .
The equation sin 4 x + cos 4 x + sin 2 x + k = 0 must have real solutions if .
Precalculus. = ( 1) 2 − 2 cos 2 x sin 2 x by the above formula ( ⋆). Class 12 MATHS DEFAULT. 5 π / 8 < x < 3 π / 4. Let u = sin^2x and dv = cos^2x dx. Luckily the problematic x x in between can be easily removed. Solve your math problems using our free math solver with step-by-step solutions. ADVERTISEMENT. sin(2(4x)) sin ( 2 ( 4 x)) Multiply 4 4 by 2 2. Put sin2x =t.
Modified 7 years, 5 months ago.
If f (x) = sin 4 x + cos 4 x in (0, The period of the curve y = sin 4 x is equal to. Solve your math problems using our free math solver with step-by-step solutions. 1 Answer. Click here:point_up_2:to get an answer to your question :writing_hand:if sin x cos x 0 then what is the value of sin4x. Biến đổi sin^4x, cos^4x Ví dụ 1: Chứng minh giá trị của biểu thức A = cos 4 x (2cos 2 x - 3) + sin 4 x (2sin 2 x - 3) không phụ thuộc vào x. cos2x − sin2x = cos2x. Verified by Toppr.
Công thức này có dạng: (sin ax)' = acos ax, trong đó a là hệ số của biến x. answered Mar 19, 2020 at 4:36. =>cos^2x=1-sin^2x. Total number of solution(s) of the equation sin 4 x + cos 4 x = 2 in
$\begingroup$ I'd like to point out: if the question then asked you to evaluate the expression given a particular value for $\sin x$, then instead of writing $\cos x=\sqrt{1-\sin^2x}$, we can simply solve for $\cos x$ using the Pythagorean theorem. Then, we have du = 2sinx cosx dx and v = (1/2)sinx + (1/4)sin3x. Antiderivative. intsin^4 (x)*cos^2 (x)=x/16-sin (4x)/64-sin^3 (2x)/48+C This integral is pretty tricky. $$3$$ Open in App. View Solution. #cos^4x-sin^4x=(cos^2x+sin^2x)(cos^2-sin^2x)=cos^2x-sin^2x=cosxcosx-sinxsinx=cos(x+x)=cos2x#
Find the range of sin 4 x + cos 4 x.
sin4(x) = −cos4(x) + 6sin2(x)cos2(x) + cos(4x) sin 4 ( x) = − cos 4 ( x) + 6 sin 2 ( x) cos 2 ( x) + cos ( 4 x) The identity is sin4(x) = 1/8(cos(4x) − 4 cos(2x) + 3) sin 4 ( x) = 1 / 8 ( cos ( 4 x) − 4 cos ( 2 x) + 3) trigonometry. Hopefully this helps! Answer link. Use the identities: a^2 - b^2 = (a - b) (a + b)) cos^2 x + sin^2 x = 1 sin^4 x - cos^4 x = (sin^2 x - cos^2 x) (sin^2 x + cos^2 x) = sin^2 x - cos ^2 x. Q2. Then f is an increasing function in the interval : View Solution. Matrix.Tech from Indian Institute of Technology, Kanpur.Once you've done that, refresh this page to start using Wolfram|Alpha.$$ The
Davneet Singh has done his B. Answer link. That's 8 extra roots Also, because you squared, you lost the information …
Trigonometry Expand the Trigonometric Expression sin (4x) sin(4x) sin ( 4 x) Factor 2 2 out of 4x 4 x. Explanation: Let #I=intsin^2xcos^4xdx#. sin2(4x)+cos2(4x) sin 2 ( 4 x) + cos 2 ( 4 x) Apply pythagorean identity. Simultaneous equation. View Solution. I'll include definitions or explanations of the rules used at the very end in the case that you would find this helpful. Apply the distributive property. View Solution.
Prove that 4(sin^4x + cos^4x)=cos4x+3 And therefore solve sin^4 + cos^4x=0. en. 2. NCERT Solutions. Arithmetic. Cooking Calculators. The total number of solution of sin4x+cos4x=sinxcosx in [0,2π) is equal to: sin4
Trigonometry. The total number of solution of the equation sin4x+cos4x=sinxcosx in [0,2π] is : Q. Differentiation. Apply the distributive property. He has been teaching from the past 13 years. 1 Answer Ratnaker Mehta Sep 4, 2016 #1/192(12x+3sin2x-3sin4x-sin6x)+C#. sin2(4x)+cos2(4x) sin 2 ( 4 x) + cos 2 ( 4 x) Apply pythagorean identity. Step 2.
Chứng minh các đẳng thức sau: sin^4x - cos^4x = 1 - 2cos^2x - Chứng minh các đẳng thức,sin^4x - cos^4x = 1 - 2cos^2x,Toán học Lớp 10,bài tập Toán học Lớp 10,giải bài tập Toán học Lớp 10,Toán học,Lớp 10.
Find the solution of the integral sin2x /sin^4x +cos^4x. Q1.
Linear equation. Solution. Substituting these values into the formula, we get:
Verify Trig Identities Tangent Solutions Trigonometric Formulas Identities Trigonometric Functions Cosine Sine Prove RELATED QUESTIONS Verify the identity cos^3xsin^2x = (sin^2x-sin^4x)cosx
Find the range of sin 4 x + cos 4 x. Viewed 869 times. cos4 (x) − sin4 (x) cos 4 ( x) - sin 4 ( x) Simplify the expression.erom dna suluclac ,yrtemonogirt ,arbegla ,arbegla-erp ,htam cisab stroppus revlos htam ruO . − 1 ≤ a ≤ 1. answered May 8, 2018 by Best answer. Guides. Simplify cos (4x)^2+sin (4x)^2. Verified by Toppr.
Could go from LHS to RHS by adding zero but I need to know how to do this WITHOUT knowing the half-angle formula. Share. f (x + π 2) = sin4(x + π 2) + cos2(x + π 2) = cos4x + sin2x.
Find the maximum and minimum values of sin 4 x + cos 4 x. asked • 04/25/19 How can I simplify this equation? sin^4 (x)-cos^4 (x) There has been several different answers for this in class. Simplify 2sin (4x)cos (4x) 2sin(4x) cos (4x) 2 sin ( 4 x) cos ( 4 x) Apply the sine double - angle identity.
integral sin^4x+cos^4x. I'll start with the left-hand side and manipulate it until it looks like the right-hand side using these two identities:
It proceeds in three steps. Answer link. tan4 x sin4 x(1 +tan4 x) = sec4 x 1 +tan4 x = (1 +tan2 x)sec2 x 1 +tan4 x. 30/12/2019 30,422.
It uses functions such as sine, cosine, and tangent to describe the ratios of the sides of a right triangle based on its angles. Enter a problem.
∫ d x (sin 4 x + cos 4 x) Recommended Questions. Đăng ký . Find all the solutions of the equation sin(4x + π 4) + cos (4x + 5π 4) = √2 which satisfy the inequality cos2x cos2 − sin2 > 2−sin4x. sin4x −cos4x = (sin2x −cos2x)(sin2x + cos2x) = sin2x −cos2x. Click here:point_up_2:to get an answer to your question :writing_hand:prove that sin 4x cos 4x 1 2cos 2x 2cos 4x. #sin2x=2sinx*cosx#
y = sin 4 x + cos 4 x = ( sin 2 x + cos 2 x) 2 − 2 sin 2 x ⋅ cos 2 x = 1 − 1 2 ( 2 sin x ⋅ cos x) 2.cos^2 x = 1 - (sin^2 2x)/2 >= 1/2 The inequality becomes: (sin^2 (2x))/2 <= 1/2 sin^2 (2x) <= 1 sin 2x <= +- 1 Solve this inequality in 2 cases: a. Therefore: sin4x −cos4x = − cos2x. $$4$$ C. A. Tap for more steps 8cos4(x)−8cos2(x)+ 2−1 8 cos 4 ( x) - 8 cos 2 ( x) + 2 - 1 Subtract 1 1 from 2 2. Solution. lim x → ∞ sin 4 x
Prove sin^{4}x- cos^{4}x=2sin^{2}x-1.eciwt $x4soc\$ dnapxe na uoy ,SHL ot SHR morf oS . sin 2x <= 1 --> The answer is undefined, because sin 2x always < 1, regardless of
The minimum value of f (x)= sin4x+cos4x,0 ≤ x ≤ π 2 is. tan4 x sin4 x(1 +tan4 x) = sec4 x 1 +tan4 x = (1 +tan2 x)sec2 x 1 +tan4 x. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. cos2 (4x) + sin2 (4x) cos 2 ( 4 x) + sin 2 ( 4 x) Rearrange terms. How to find the Value of Sin4x, Cos4x, Cot4x? The value of sin4x is 8 sinx cos3x - 4 sinx cosx, the value of cos4x is 4 cos4x - 8 cos2x + 1, and the value of cot4x is (tan4x - 6tan2x + 1)/ ( 4 tanx (1 - tan2x). Cooking Calculators.
View Solution. answered May 29, 2021 by Zafaa (30. 4(sin(x)cos(x))cos(2x) 4 ( sin ( x) cos ( x)) cos ( 2 x)
Linear equation. Cách giải phương trình lượng giác cơ bản đưa ra phương pháp và các ví dụ cụ thể, giúp các bạn học sinh THPT ôn tập và củng cố
I = ∫ π 2 0 xsinxcosx sin4x+cos4x --- (1) I = ∫ π 2 0 ((π 2−x)cosxsinx) cos4 +sin4x dx --- (2) Adding (1) and (2), we get. 5π 4 < x< 3π 4. which has a period of. = ( sin 2 x) ( sin 2 x) − ( cos 2 x) ( cos 2 x) = ( sin 2 x) 2 − ( cos 2 x) 2 = ( sin 2 x − cos 2 x) ( sin 2 x + cos 2 x) = ( sin 2 x − cos 2 x) ( 1) = sin 2 x − cos 2 x Is that true? trigonometry Share Cite Follow edited Sep 4, 2017 at 4:34
2 Answers Mia · shr Aug 29, 2016 (sinx −cosx)(sinx + cosx) Explanation: Factorizing this algebraic expression is based on this property: a2 −b2 = (a −b)(a +b) Taking sin2x = a and cos2x = b we have : sin4x −cos4x = (sin2x)2 − (cos2x)2 = a2 −b2 Applying the above property we have: (sin2x)2 −(cos2x)2 = (sin2x −cos2x)(sin2x + cos2x)
Trigonometry Nick K. Use the double - angle identity to transform cos(2x) cos ( 2 x) to 2cos2(x)−1 2 cos 2 ( x) - 1. / 4 < x < 3 π / 8. B.
If cos4x cos2y + sin4x sin2y = 1, Prove that cos4y cos2x + sin4y sin2x = 1. I = `int ( 1 + t^2)/(1+ t^4) dt`
Hàm số y=sin^4x-cos^4x đạt giá trị nhỏ nhất tại x=x0 mệnh đề nào. Where c is any constant involved, dx is the coefficient of integration and ∫ is the symbol of the integral. Câu hỏi. View Solution. Practice Makes Perfect. Study Materials.
Step by step video & image solution for the period of the f(x)=sin^4x+cos^4x is by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Giải phương trình lượng giác sin4x; cos4x. Open in App. So from RHS to LHS, you an expand $\\cos4x$ twice. Share. Just like running, it takes practice and dedication.
Click here:point_up_2:to get an answer to your question :writing_hand:evaluateint sin4 x cos4x dx
Tìm hiểu thêm. Extended Keyboard Examples Upload Random. Updated on: 21/07/2023. Simplify 2sin (4x)cos (4x) 2sin(4x) cos (4x) 2 sin ( 4 x) cos ( 4 x) Apply the sine double - angle identity.
Free trigonometric simplification calculator - Simplify trigonometric expressions to their simplest form step-by-step. Tap for more steps
Join Teachoo Black. en. Q 5. Điều này cho chúng ta biết rằng tỷ lệ biến đổi của hàm sin 4x
cos2(θ) = 1 2 (1 + cos(2θ)) Answer link.
In summary, the conversation discusses whether or not the equation cos^4x + sin^4x = 1 is true. sin 4 x + cos 4 x = a. Trang chủ. 1 Answer +1 vote . Enter a problem. sin4(x) +cos4(x) = cos(4x) + 3 4 sin 4 ( x) + cos 4 ( x) = cos ( 4 x) + 3 4. I = ∫ 2 sin x cos x sec 4 x (sin 4 x + cos 4 x)
Precalculus.
Question Integrate: ∫ 1 sin4x +cos4xdx Solution Verified by Toppr I = ∫ 1 sin4x+cos4xdx = ∫ sec4x 1+tan4xdx Let tanx = t ⇒ sec2xdx =dt I = ∫ (1+t2) 1+t4 dt = ∫ t2(1+ 1 t2) t2(t2 + 1 t2)dt = ∫ 1+ 1 t2 t2 + 1 t2−2+2dt Let t− 1 t = v ⇒ (1+ 1 t2)dt = dv I = ∫ dv (√2)2 +v2 = 1 √2tan−1( v √2)+c = 1 √2tan−1[ tan2x+1 √2tanx]+c. Similar Questions. I get as close as $$\frac{ \cos^4
Ex 7.
π 4 < x < 3 π 8. D. 3 π / 8 < x < 5 π / 8. sin^4x+cos^4x. Related Symbolab blog posts. D. Find all the solutions of the equation sin(4x + π 4) + cos (4x + 5π 4) = √2 which satisfy the inequality cos2x cos2 − sin2 > 2−sin4x. \sin^4x-\cos^4x=(\sin^2x-\cos^2x)(\sin^2x+\cos^2x)=-\cos 2x So, \frac{d(\sin^4x
What is the formula of cos4x? Get the answer to this question and access a vast question bank that is tailored for students. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Q1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just
Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Was this answer helpful? 29
derivative sin^4x+cos^4x.
Explanation: We will use Pythagoras' identity: sin2x +cos2x = 1. sin(2(4x)) sin ( 2 ( 4 x)) Multiply 4 4 by 2 2. It's going to require the use of a few trigonometric identities and rules for integration. It is a bit involved, but we can use u-substitution to find the integral of sin^4(x). Solve your math problems using our free math solver with step-by-step solutions. edited Apr 13, 2017 at 12:20.1.
Solve Solve for x x = 2π n1 n1 ∈ Z Graph Graph Both Sides in 2D Graph in 2D Quiz Trigonometry sin4x+cos4x= cos4x Similar Problems from Web Search Is sin4 x − cos4 x = cos2x or is it −cos2x = cos2x?
How do you use the power reducing formulas to rewrite the expression sin4xcos4x in terms of the first power of cosine? 1281 (3−4cos(2x)+cos(4x)) Explanation: Use sin2A = 2sinAcosA , sin2A = 21(1 −cos2A) and cos2A= 21(1+cos2A)
Trigonometry Expand the Trigonometric Expression sin (4x) sin(4x) sin ( 4 x) Factor 2 2 out of 4x 4 x. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. Tap for more steps (cos2(x))2 −(sin2 (x))2 ( cos 2 ( x)) 2 - ( sin 2 ( x)) 2.
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Practice Makes Perfect. C. Explanation: Investigate the sign of f ′(x) on the interval [0, 2π] f ′(x
Factor 2 2 out of 4x 4 x. Let u = sin^2x and dv = cos^2x dx.maxe 0202 EEJ rof retteb eraperp dna snoitseuq shtaM detimilnu htiw gnola noitseuq siht ot rewsna eht dniF . Use the identities: a2 −b2 = (a −b)(a +b)) cos2x + sin2x = 1. answered • 04/25/19 Tutor 5. Learning math takes practice, lots of practice. ∫ 1 +t2 1 +t4 dt= 1 2 ∫[ 1 t2 − 2-√ t + 1
Precalculus. Simplify each term. Natural Language. Spinning The Unit Circle (Evaluating Trig Functions ) If you've ever taken a ferris wheel ride then you know about periodic motion, you go up and down over and over Read More. Q.
By making use of black magic, the resolution transformed $$(\sin^4 x + \cos^4x)$$ into $$(\sin^4 x + \cos^4x)=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x$$ Analysing and transforming the terms with the identities, one reaches that these two terms could be rewritten as: $$1-\sin^22x$$ The rest of the question was very straightforward, simple algebra to
My trial is listed below $$\sin^4x+\cos^4x=\\(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x=\\1-2(\frac{\sin^2(2x)}{2}) Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Cooking Calculators. 3π 8 < x< 5π 8. en. Standard XII. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Just like running, it takes practice and dedication.
If cos4x cos2y + sin4x sin2y = 1, Prove that cos4y cos2x + sin4y sin2x = 1. Đăng nhập + Hỏi cộng đồng +
sin^4(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Period of cos2x = π. Similar Questions. Q 4.com tổng hợp và xin gửi tới bạn đọc cùng tham khảo, mời các bạn cùng tham khảo chi tiết tại đây nhé. Cite. Solve ∫ cos4x−cos4x sin4x−sin2xdx. Solve the following equations.
Mar 19, 2018. Solution. 9 videos. 1 1. Enter a problem. Verified by Toppr.sin 4 x + cos 4 x I should rewrite this expression into a new form to plot the function. Science Anatomy & Physiology Astronomy Astrophysics
Click here:point_up_2:to get an answer to your question :writing_hand:find 3left sin 4xcos 4x right 2leftsin6xcos6xright. Enter a problem. sin(2(2x)) sin ( 2 ( 2 x)) Apply the sine double - angle identity. Find the interval in which the given function increases. Click here:point_up_2:to get an answer to your question :writing_hand:let fx sin4x cos4x then f is an. Best answer
The graph of y_1 = sin^4x- cos^4x and y_2 = cos(3x) confirms that the solutions are the intersection points. sin^4x+cos^4x. So could you please help me out. lim x → ∞ sin 4 x
Prove sin^{4}x- cos^{4}x=2sin^{2}x-1. Join / Login. Arithmetic. Hàm số y = sin4x−cos4x y = sin 4 x - cos 4 x đạt giá trị nhỏ nhất tại x = xo x = x o. indefinite integral; class-12; Share It On Facebook Twitter Email. Inequality always true. ⇒ 2sinxcosxdx =dt. Apply the sine double - angle identity.noitutitsbus girt esrevni na gnisu noitcnuf lanoitar a ot dnargetni eht trevnoC . If you want Read More.1. What are the 3 types of trigonometry functions? The three basic trigonometric functions are: Sine (sin), Cosine (cos), and Tangent (tan). (2) (2) tan 4 x sin 4 x ( 1 + tan 4 x) = sec 4 x 1 + tan 4 x = ( 1 + tan 2 x) sec 2 x 1 + tan 4 x. $$7$$ D. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.5 for 0 Get the answers you need, now!
Evaluate: ∫ (xsinxcosx)/(sin 4 x+cos 4 x)dx for x →[0, π/2] integral calculus; class-12; Share It On Facebook Twitter Email. (sinx-cosx) (sinx+cosx) Factorizing this …
If you don't know how, you can find instructionshere. C. Đăng nhập +
Integration by Parts Method: To solve the integral of sin^4x cos^2x using integration by parts, we can use the following formula: ∫u dv = uv - ∫v du.5k points) selected May 30, 2021 by rahul01 . Then, we have du = 2sinx cosx dx and v = (1/2)sinx + (1/4)sin3x. Practice Makes Perfect. Simplify cos (4x)^2+sin (4x)^2. ∫ s i n x c o s x s i n 4 x + c o s 4 x d x = View Solution. B. 0 < a ≤ 1. en. Giải phương trình sin^4x+cos^4x=1/2. Limits. Open in App. Use the double-angle identity to transform to .1k points) selected Sep 19, 2019 by faiz . C. Follow. D. NCERT Solutions For Class 12. 2π 4 = π 2 2 π 4 = π 2. Community.The integration of sin 4x is equal to the negative of one-fourth of the cosine of the angle 4x plus the constant of integration which is mathematically written as ∫sin 4x dx = (-1/4) cos 4x + C, where C is the constant of integration
Find the value of sin 4 x given that cos(2x) = 1/5. Since the given sine function has an exponent to the fourth power, express the equation sin 4 x as a squared term. We've covered methods and rules to differentiate functions of the form y=f(x), where y is explicitly defined as Read More. Math Input.
Sin 4x is a trigonometric function of sine with an angle of 4x. Tìm thêm: Sin 4x Cos 4x Giải phương trình lượng giác sin4x ＋ cos4x = 1/2sin2x Giải phương trình sin4x ＋ cos4x = 1/2sin2x. Answer link. B.2. 0< x < π 8. Verified by Toppr. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Therefor, f (x) = cos2x. View Solution. Can you run with that idea?
What is the integral of #sin^2(x)cos^4(x) #? Calculus Introduction to Integration Integrals of Trigonometric Functions. Advanced Math Solutions - Derivative Calculator, Implicit Differentiation. Related Symbolab blog posts. (sin2x + cos2x) = 1. 0 votes .Once you've done that, refresh this page to start using Wolfram|Alpha. Solution. Rewrite as . Expand using the FOIL Method.
Total number of solution (s) of the equation sin4x+cos4x =2 in [−2π,2π] is : View Solution. From what I know of of $\sin$ and $\cos$ functions, this fits the pattern I observe in calculating the derivatives of $\sin^4 x + \cos^4 x$. If you want Read More. Factor out of .
Linear equation. − 1 ≤ a ≤ 1. sin4(x) +cos4(x) = cos(4x) + 3 4 sin 4 ( x) + cos 4 ( x) = cos ( 4 x) + 3 4. Đạo hàm y=sin^4x+cos^4x. Q3. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just
Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Open in App.1 ≤ a ≤ 2 1 . Natural Language. Click here:point_up_2:to get an answer to your question :writing_hand:find the maximum and minimum values of fxsin 4 x cos. A. Angina Seng.
My concerns. Follow edited Mar 19, 2020 at 4:45. I = π 8∫1 0 dt 2t2 −2t+1 ⇒I = π 16∫ dt t2 −t+ 1 2. B. #cos2x=1-2sin^2x# #sin^2x=(1-cos2x)/2# and. Integration of sin 4x can be calculated using different methods such as the substitution method.
The problem is to solve $$\int \sin(4x Stack Exchange Network. Use app Login.3, 10 Integrate the function 𝑠𝑖𝑛4 𝑥 ∫1 sin^4𝑥 𝑑𝑥 =∫1 (sin^2𝑥 )^2 𝑑𝑥 =∫1 ((1 − cos2𝑥)/2)^2 𝑑𝑥 =1/4 ∫1 (1−cos2𝑥 )^2 𝑑𝑥 We know that 𝑐𝑜𝑠2𝜃=1−2 〖𝑠𝑖𝑛〗^2𝜃 2 〖𝑠𝑖𝑛〗^2𝜃=1−𝑐𝑜𝑠2𝜃 〖𝑠𝑖𝑛〗^2𝜃=(1 − 𝑐𝑜𝑠2𝜃)/2 Replace 𝜃 by 𝑥
After some nice trig manipulations, you can find that. May 7, 2015. Q2. Đồ thị hàm số y=sin^4x+cos^4x. We will use the following Identities to simplify the Integrand :-
Integration of x sin6 x cos4 x x sin 6 x cos 4 x.noituloS weiV . sin(8x) sin ( 8 x) Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like
Explanation: f (x) = cos4x − sin4x = (cos2x −sin2x)(cos2x +sin2x) Reminder of trig identities: cos2x − sin2x = cos2x. Then we have. …
sin 4x = sin2(2x) We know that, sin 2x = 2 sinx cosx. Learning math takes practice, lots of practice. $$5$$ B. Just like running, it takes practice and dedication. When this is zero, this makes the equation satisfied automatically. Q 5. Cite. View Solution. Misc 25 Evaluate the definite integral ∫_0^ (𝜋/4) 〖 (sin𝑥 cos𝑥)/ (cos^4𝑥 + sin^4𝑥 ) 𝑑𝑥〗 ∫_0^ (𝜋/4) 〖 (sin𝑥 cos𝑥)/ (cos^4𝑥 + sin^4𝑥 ) 𝑑𝑥〗 Adding and subtracting 2 〖𝑠𝑖𝑛〗^2 𝑥 〖𝑐𝑜𝑠〗^2 𝑥 from denominator = ∫_0^ (𝜋/4
The equation sin 4 x + cos 4 x = a has a real solution, if .
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If you don't know how, you can find instructionshere. Share. jee mains; jee; Share It On Facebook Twitter Email. It will be much easier to write the fourth power of the sine function in terms of squared power to avoid the use of the half-angle identities and double-angle identities. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get …
sin4(x) = (sin4x)1. …
(sin 4 x - cos 4 x) = (sin 2 x) 2 - (cos 2 x) 2 = [(sin 2 x + cos 2 x)(sin 2 x - cos 2 x)]. The total number of solution of the equation sin4x+cos4x=sinxcosx in [0,2π] is : Q. Similar Questions. Learning math takes practice, lots of practice. answered Sep 19, 2019 by Deepak01 (59. Therefore, sinxcosxdx = dt 2. View Solution. sin 4 x + cos 4 x = a. 1 4 ≤ a ≤ 1 2.
A. Physics. 1 1.3. View Solution. Differentiation. Math Input. Find the maximum and minimum values of f (x)= cos(x+ π 3)+2√2sin(x+ π 3)−3. As the function is of the form sin 2 n x + cos 2 n x. Including 1, -1, -cos (2x), and unable to simplify? Thanks! Follow • 2 Add comment Report 1 Expert Answer Best Newest Oldest Darryl B. Hàm số lượng giác lớp 11 đưa ra phương pháp và các ví dụ
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Tìm GTNN và GTLN của biểu thức - Cho y = sin^4x + cos^4x,Tìm GTNN và GTLN của biểu thức,Toán học Lớp 11,bài tập Toán học Lớp 11,giải bài tập Toán học Lớp 11,Toán học,Lớp 11. 8cos4(x)−8cos2(x)+ 1 8 cos 4 ( x) - 8 cos 2 ( x) + 1
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Trigonometry Expand the Trigonometric Expression cos (4x) cos (4x) cos ( 4 x) Factor 2 2 out of 4x 4 x. Also note that the difference of squares identity can be written: A2 − B2 = (A− B) We can use this with A = sin2x and B = cos2x as follows: sin4x −cos4x = (sin2x)2 − (cos2x)2. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. This gives ∫2π 0 dx sin(x)4 + cos(x)4 = 2∫2π 0 dx 1 + cos(2x)2 = 8∫π / 2 0 dx 1 + cos(2x)2. sin^4 x + cos^4 x = (sin^2 x + cos^2 x)^2 - 2sin^2 x. Solve the following equations. Differentiation. Bộ đề. A. Learning math takes practice, lots of practice. 1 Answer +1 vote . $$\frac{\sin x \cos x}{\sin^4x + \cos^4x} = \frac{\sin x \cos x}{(1-\cos^2x)^2 + \cos^4x}\\=\frac{\sin x \cos x}{2\cos^4x -2\cos
The function f (x) = sin 4 x + cos 4 x increasing if. Giải phương trình sin^6x+cos^6x=1/4. As the function is of the form sin 2 n x + cos 2 n x.
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C. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Limits. I feel uncomfortable putting so much weight on observing a pattern, instead I feel I should be able to put it down in terms of mathematics. edited Mar 11, 2018 at 7:48. Class 12 MATHS QUESTION BANK. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, $$\int \sin(4x)(1+\cos(4x)) \mathrm dx$$
Let I = `int 1/(cos^4x+sin^4x) dx` Divide numerator and denominator by cos 4 x, we get: `int [sec^4x]/[1 + tan^4x]` dx `int [sec^2 x(sec^2x)]/[ 1 + tan^4x ]` dx `int [sec^2 x( 1 + tan^2 x)]/( 1 + tan^4x )`dx. 2I = π 2∫ π 2 0 sinxcosx sin4x+cos4xdx. Letting t = tan x t = tan x, the integral turns out to be. Let's check period for smaller value π 2. Mệnh đề nào sau đây là đúng?
If sin4x+cos4y+2 = 4sinxcosy and 0 ≤x, y ≤ π 2 then sinxcosy is equal to. Related Symbolab blog posts. ⇒ 2I = π 2× 1 2∫ 1 1 dt t2 +(1−t)2. complex-numbers. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…
If f (x) = cos2x+sin4 x sin2x+cos4 x for x ∈ R then f (2002) is equal to. Letting t = tan x t = tan x, the integral turns out to be. Đăng ký . Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Click here:point_up_2:to get an answer to your question :writing_hand:prove that sin 4x cos 4x 1 2cos 2x 2cos 4x. f (x) = sin 4 x + cos 4 x
The function f (x) =sin4x+cos4x increases if. Q5. View Solution. Enter a problem.3, 10 Integrate the function 𝑠𝑖𝑛4 𝑥 ∫1 sin^4𝑥 𝑑𝑥 =∫1 (sin^2𝑥 )^2 𝑑𝑥 =∫1 ((1 − cos2𝑥)/2)^2 𝑑𝑥 =1/4 ∫1 (1−cos2𝑥 )^2 𝑑𝑥 We know that 𝑐𝑜𝑠2𝜃=1−2 〖𝑠𝑖𝑛〗^2𝜃 2 〖𝑠𝑖𝑛〗^2𝜃=1−𝑐𝑜𝑠2𝜃 〖𝑠𝑖𝑛〗^2𝜃=(1 − 𝑐𝑜𝑠2𝜃)/2 Replace 𝜃 by 𝑥
After some nice trig manipulations, you can find that. Use the chain rule to differentiate both terms The chain rule states f' (g (x)) = f' (x)*g' (x) We can let f (x) = x^4 and g (x) = sin (x), thus f (g (x)) = sin^4 (x) Similarly, we can let h (x) = cos (x) and so f (h (x)) = cos^4 (x) So then
Step by step video & image solution for int (sin^4x-cos^4x)dx is equal to by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Toán. edited Apr 13, 2017 at 12:20. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…
Solve your math problems using our free math solver with step-by-step solutions. If you want Read More. Lớp 11. Login.
Nghi N. cos2 (4x) + sin2 (4x) cos 2 ( 4 x) + sin 2 ( 4 x) Rearrange terms. cos(α+β) = cos(α)cos(β)−sin(α)sin(β) How do you find the intervals in which the function f (x) = sin4x + cos4x is increasing and decreasing in [0, 2π] Please see below. cos(2(2x)) cos ( 2 ( 2 x)) Simplify each term. ∫ 1 +t2 1 +t4 dt= 1 2 ∫[ 1 t2 − 2–√ t + 1
Explanation: The identity needed is the angle-sum identity for cosine. Let I= ∫ (xsinxcosx)/(sin 4 x+cos 4 x)dx for x →[0, π/2] [Dividing numerator and denominator by cos 4 x]
First, some preliminary manipulation. Related Symbolab blog posts. D. 0 < x < π / 4. D.
Solve your math problems using our free math solver with step-by-step solutions. Simultaneous equation.xd x4soc x 4nis tnietaulave ️ noitseuq ruoy ot rewsna na teg ot👆ereh kcilC
. 1 2 ≤ a ≤ 1. While it can be written as cos^4x + sin^4x = (cos^2x + sin^2x)^2 - 2cos^2xsin^2x, it is not a correct form. Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter See more. Related Symbolab blog posts. E. 0 energy points. Practice Makes Perfect. B. Cooking Calculators. π. Cite. Multiply 2 2 by 2 2. Substituting these values into the formula, we get:
Verify Trig Identities Tangent Solutions Trigonometric Formulas Identities Trigonometric Functions Cosine Sine Prove RELATED QUESTIONS Verify the identity cos^3xsin^2x = (sin^2x-sin^4x)cosx
We use the following identities. Hopefully this helps! Trigonometry . Đăng ký . Click here:point_up_2:to get an answer to your question :writing_hand:displaystyle int frac sin 2x. See my answer. Tap for more steps Step 2. Follow. cos 2x f (x) = cos^4x - sin^4 x = (cos^2 x - sin^2 x) (cos^2 x + sin^2 x) Reminder of trig identities: cos^2 x - sin^2 x = cos 2x (sin^2 x + cos^2 x) = 1 Therefor
Q. Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (a+b)(a−b) a 2 - b 2 = ( a + b) ( a - b) where a
Integral of sin^4(x) Google Classroom. Integration. Thus, sin2(2x) = 2 sin2x cos2x = 2 (2 sinx cosx) cos2x = 4 sinx cosx (2cos 2 x - 1) [ Since, cos2x = 2cos 2 x - 1] = 8 sinx cos 3 …
Trigonometry Expand the Trigonometric Expression cos (4x) cos (4x) cos ( 4 x) Factor 2 2 out of 4x 4 x. Giá trị lớn nhất, giá trị nhỏ nhất của hàm số y=sin^4x+cos^4x.
Explanation: The period of given function: f (x) = sin4x + cos2x. Reduce the integral using the half-angle formulae and periodicity considerations. Question. Đăng nhập +
Integration by Parts Method: To solve the integral of sin^4x cos^2x using integration by parts, we can use the following formula: ∫u dv = uv - ∫v du.
cos^4(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.cos^2 x = = 1 - 2sin^2 x.
Then I use the binomial theorem to expand this fourth power, and comparing real and imaginary parts, I conclude that $\cos^4 x + \sin^4 x = \cos (4x) + 6 \cos^2 (x) \sin^2 (x)$.
math program.3. Click here:point_up_2:to get an answer to your question :writing_hand:the period of sin4x cos4x is.
The answer is =sin^2x We need sin^2x+cos^2x=1 a^2-b^2=(a+b)(a-b) a^4-b^4=(a^2+b^2)(a^2-b^2) The expression is sin^4x-cos^4x+cos^2x =(sin^2x+cos^2x)(sin^2x-cos^2x)+cos
The function f (x) =sin2x+cos2x ∀x ∈ [0, π 2] is strictly decreasing in the interval. Start with: sin^2x+cos^2x=1 and cos2a=cos^2x-sin^2x 2. Solve. Using complex analysis, it can be shown that cos^4x + sin^4x = cos(4x) = (x^4 + y^4)/r^4, which is not equal to 1. = cos 2 x
Sin 4 x+cos 4 x = (sin²x) 2 + (cos²x) 2 = sin 2 x + 2sin²xcos²x + cos 2 x - 2sin²xcos²x = (sin 2 x + 2sin²xcos²x + cos 2 x) - 2sin²xcos²x = (sin²x + cos²x)² - 2sin²xcos²x = 1 - 2sin²xcos²x = = = B.
Trigonometry - Find The Range of sin^4x + cos^4x
cos 4 x-sin 4 x Formula To simplify the expression cos 4 x -sin 4 x, we first apply the formula a 2 -b 2 = (a-b) (a+b) with a = cos 2 x and b = sin 2 x. Sin 4x Cos 4x vừa được VnDoc. sin ( 4 x) + c. LCM (π,π) = π. So the …
The equation sin 4 x + cos 4 x = a has a real solution, if . Open in App.fo doirep a sah hcihw . Integration. If the point
dy dx = 2sin(2x) This is because the derivative of −cosa = a'sina. (2) (2) tan 4 x sin 4 x ( 1 + tan 4 x) = sec 4 x 1 + tan 4 x = ( 1 + tan 2 x) sec 2 x 1 + tan 4 x. $\endgroup$
Multiply (1) ( 1) by tan4 x tan4 x tan 4 x tan 4 x we obtain. Áp dụng công thức này vào hàm số sin 4x, chúng ta sẽ có: (sin 4x)' = 4cos 4x. Verified by Toppr. Q 5. The total number of solution of sin4x+cos4x=sinxcosx in [0,2π) is equal to: sin4
Trigonometry. sin(8x) sin ( 8 x) Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like
Q. I am able to solve sin6 xcos4 x sin 6 x cos 4 x.
Answer link.
Chứng minh các đẳng thức sau: sin^4x - cos^4x = 1 - 2cos^2x - Chứng minh các đẳng thức,sin^4x - cos^4x = 1 - 2cos^2x,Toán học Lớp 10,bài tập Toán học Lớp 10,giải bài tập Toán học Lớp 10,Toán học,Lớp 10. Verified by Toppr. Tap for more steps
Expand the Trigonometric Expression cos(4x) Step 1. D. But there is a x x in between. Giải phương trình sin^4x+cos^4x=1. 2(2sin(x)cos(x))cos(2x) 2 ( 2 sin ( x) cos ( x)) cos ( 2 x) Multiply 2 2 by 2 2. C. Limits. B. π 4< x< 3π 8. Solution. Open in App. So now I need to show that $\cos (4x) + 6 \cos^2 (x) \sin^2 (x)=\frac{1}{4} \cos (4x) +\frac{3}{4}$, which has stumped me. ∫sin7 xcos4xdx ∫ sin 7 x cos 4 x d x. Cite. complex-analysis;
On the other hand, using the double angle formulas for $\sin$ and $\cos$ (or just their complex representations) shows that the integrand has period $\frac{\pi}{2}$; using this observation and the symmetry of the integrand gives $$\int_0^{2 \pi} \frac{dx}{\sin^4 x + \cos^4 x} = 8 \int_0^{\frac{\pi}{4}} \frac{dx}{\sin^4 x + \cos^4 x} . I get as close as $$\\frac{ \\cos^4
Ex 7. View Solution. Similar Questions. It has been given as, ∫π 0 xsin6 xcos4 xdx ∫ 0 π x sin 6 x cos 4 x d x. Related Symbolab blog posts. Simplify cos (x)^4-sin (x)^4. where we use the relation ( a + b) 4 = a 4 + …
Explanation: sin4x −cos4x = (sin2x +cos2x)(sin2x − cos2x) Reminder: sin2x +cos2x = 1, and. Find 3 (sin 4 x + cos 4 x)
A little simplification of the given expression would ease of the differentiation. Multiply cos(x) cos ( x) by cos2 (x) cos 2 ( x) by adding the exponents. $$5$$ Given $$1+\sin^4 x=\cos^2 3 x$$ As $$\sin^4 x\in [0,1]\implies 1+\sin^4 x\in [1,2]$$
Evaluate ∫ (sinx + cosx)/(sin 4 x + cos 4 x) dx \(\int\frac{sin\,x+cos\,x}{sin^4x + cos^4x}\) dx. Answer. ∫ s i n x c o s x s i n 4 x + c o s 4 x d x = View Solution. Let f (x) =sin4x+cos4x.
In mathematical form, the integral of cos^4x is: ∫ cos 4 x d x = 3 x 8 + 1 4 sin ( 2 x) + 1 32. sin4 x 2 − cos4 x 2 = 1 4. Rearrange both: sin^2x=1-cos^2x and cos^2x=cos2x+sin^2x
The number of solutions of the equation $$1+\sin^4x=\cos^23x, x\in \left[-\dfrac{5\pi}{2}, \dfrac{5\pi}{2}\right]$$ is? A. About About this video Transcript. Solve the following equations. If you want Read More. C. from which we can deduce: sin2x = 1 − cos2x. Step 2. Tập xác định của hàm số y=sin^4x+cos^4x. Solution. Find all the solutions of the equation sin(4x + π 4) + cos (4x + 5π 4) = √2 which satisfy the inequality cos2x cos2 − sin2 > 2−sin4x. sin(2(2x)) sin ( 2 ( 2 x)) Apply the sine double - angle identity. Integration. View Solution. Solve the following equations. To prove that cos^4x-sin^4x=1-2sin^2x, we'll need the Pythagorean identity and a variation on the Pythagorean identity: color (white)=>cos^2x+sin^2x=1. Misc 25 Evaluate the definite integral ∫_0^ (𝜋/4) 〖 (sin𝑥 cos𝑥)/ (cos^4𝑥 + sin^4𝑥 ) 𝑑𝑥〗 ∫_0^ (𝜋/4) 〖 (sin𝑥 cos𝑥)/ (cos^4𝑥 + sin^4𝑥 ) 𝑑𝑥〗 Adding and subtracting 2 〖𝑠𝑖𝑛〗^2 𝑥 〖𝑐𝑜𝑠〗^2 𝑥 from denominator = …
To simplify the expression cos 4 x+sin 4 x, we first apply the formula a 2 +b 2 = (a+b) 2 -2ab with a = cos 2 x and b = sin 2 x. Giải phương trình sin^6x+cos^6x=1. cos(2(2x)) cos ( 2 ( 2 x)) Simplify each term. Correct option is A. 1 4 ≤ a ≤ 1 2. Q 5. Matrix. Share. f x = sin 4 x + cos 4 x ⇒ f ' x = 4 cos x sin 3 x-4 cos 3 x sin x ⇒ f ' x = 4 cos x sin x sin 2 x-cos 2 x ⇒ f ' x =-2 sin 2 x cos 2 x ∵ sin 2 θ-cos 2 θ = cos 2 θ and sin 2 θ = 2 sin θ cos θ ⇒ f
Q 5. Therefore, cos 4 x − sin 4 x = ( cos 2 x) 2 - ( sin 2 x) 2 = ( cos 2 x − sin 2 x) ( cos 2 x + sin 2 x) = cos 2 x ⋅ 1 by the above formulas ( ⋆) and ( ⋆ ⋆). Class 12 MATHS INTEGRALS. Vậy đạo hàm của hàm số sin 4x theo biến số x là 4cos 4x.
Find the intervals in which the function f given by f (x) = sin 4 x + cos 4 x, x ∈ [0, π / 2] is (a) is decreasing (b) is increasing Also, state whether x = π / 4 is a point of local minima or local maxima ?
Prove cos^{4}x - sin^{4}x = cos2x. 2π 4 = π 2 2 π 4 = π 2. Simultaneous equation. #a^(2n)-b^(2n)=(a^n+b^n)(a^n-b^n)# #sin^2x+cos^2x=1# #cos(a+b)=cosacosb-sinasinb# Proof.
$\int{\frac{\cos^4x + \sin^4x}{\sqrt{1 + \cos 4x}}dx}$ given that $\cos 2x \gt 0$ I tried to simplify this, but I cannot seem to proceed further than the below Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share
The value of x in (0,π/2) satisfying the equation √3−1 sinx + √3+1 cosx = 4√2. 0 < a ≤ 1. Jokes apart, sin4(x) = (1 − cos2(x))2 = (1 − cos(2x) 2)2 = 1 4 − cos(2x) 2 + cos2(2x) 4 hence: sin4(x) = 3 8 − cos(2x) 2 + cos(4x) 8 = 3 − 4cos(2x) + cos(4x) 8. ∫sin7 xcos4xdx = ∫(sin2 x)3cos4x sin xdx = ∫(1 −cos2 x)3cos4x sin xdx, u = cos x, du = − sin xdx = − ∫(1 −u2)3u4xdu = − ∫(1 − 3u2 + 3u4 −u6)u4du =u4 − 3u6 + 3u8 −u10 = u5 5 − 3u7 7 + 3u9 9 − u11 11 + c ∫ sin 7 x cos 4
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#intsin^4x*cos^2x dx=int(sin^2x)*(sin^2x*cos^2x)dx# #=int(1/2) * (1-cos2x) * ((sin2x)/2)^2dx# We have. Community.
$\begingroup$ I'd like to point out: if the question then asked you to evaluate the expression given a particular value for $\sin x$, then instead of writing $\cos x=\sqrt{1-\sin^2x}$, we can simply solve for $\cos x$ using the Pythagorean theorem. Putting tan x = t, Sec 2 x dx = dt. Just like running, it takes practice and dedication. Expand in terms of complex exponentials. Tap for more steps Step 2. I have just applied the Pythagorean theorem ( sin2z + cos2z = 1) and twice the cosine duplication formula ( cos(2z) = 2cos2z − 1, giving cos2(z) = 1
Could go from LHS to RHS by adding zero but I need to know how to do this WITHOUT knowing the half-angle formula.. Enter a problem. Solution. Step by step video & image solution for int(dx)/((sin^4x+cos^4x) by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. The condition tells us that equality holds, thus we have $\frac{ \sin^2 x } { a} = \frac{ \cos^2 x } { b}$. The above formula can also be used to calculate the integral of cos^3x. View Solution. sin 4 x + cos 4 x = (sin 2 x + cos 2 x) 2 - 2 sin 2 x cos 2 x
$\frac{ \sin^4 x}{ a} + \frac{ \cos^4 x } { b} \geq \frac{ ( \sin^2 x + \cos^2 x)^2 } { a + b } = \frac{1}{a+b}$. ∫ sin 2x sin4x+cos4xdx is equal to tan−1(f (x)n)+C, then which of the following is/are correct ? View Solution. Follow. Arithmetic. Step 2.