Prove the identity. 9 sin(x – y) cos(x) cos(y) 9 tan(x) – 9 tan(y) %3D Use a Reciprocal Identity, and then rewrite as a single rational expression. 9 sin(y) cos(y) 9 tan(x) - 9 tan(y) %3D cos(x) cos(x) cos(y) Use an Addition or Subtraction Formula to simplify. %3D

Q: x/4 The definite integral sin24x cos2x dx is equivalent to x/2 1 -sin20 cos20 de A x12 2sin20 cos40…

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Q: (-1)" (2n+1)! Given: sin x = En=0 x2n+1 for x e R 100 What is the exact value of the sum 2n=0…

A: The series given is: sin x=∑n=0∞(-1)nx2n+1(2n+1)!, x∈ℝ...(1) To find the exact value of the series…

Q: The integral of the given function | cos(9x) cos(5x)dx is equal .. 14 sin 4x + 4 sin 14x А. · + C 12…

A: This question can be solved by applying the formula of 2.cosA.cosB

Q: Please answer #40.  *Rewrite the expression with no exponent higher than 1.

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Q: 2. Find the value of e a. 2 sin2 0 - sin 0 - 1 = 0

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Q: 2. * S 4 (;- e-²) cos (e-2 + Inz) dz 4 sin (e-z + In z) + C A C sin (e-Z + In z) + C B 4 sin (; -…

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Q: 3. Iim Sin 5x (-) (+) fcx) fcx) - 0-2 o. 84147 0.2 0.24147 -0.02 0.99833 0.02 0.99833 -D.002 0.…

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Q: e the substitution formula to evaluate the integral. 27 27) 3 cos2 x sin x dx T/3 21 C)-- A)- 129 D)…

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Q: 2х dx cos?(2x) Evaluate 1. xtan (2x) + In|cos(2x)| + C 1 xtan (2x) + In|sec(2x)} + C xtan (2x) 1…

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Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

A: Here I am attaching image so that you understand each and every step.

Q: (-1)" x2n+1 En=0 (2n+1)! Given: sin x = for x ER Determine the exact value of the sum Σ (-1)"(2n +…

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Q: 212 sin(k/n). lim 1. cos(1) + 5/3 2 cos(1) +1/3 +2/3

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Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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Q: Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x)…

A: Given identity for proof is  Sinh(x+y) = Sinh(x)Cosh(y)+ Cosh(x)Sinh(y)

Q: sin²x dx cos x

A: To decompose the given integral we have to use some basic trigonometric formulas.   We know that,…

Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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Q: f (0. 80108) = sin 3 (0. 80108) + cos 2 (0. 80108) – (0. 80108)²

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Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

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Q: 2. Find the antiderivative of COS -2 sin a Simplify dr

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Q: +oo (-1)"n" sin" () ' Σ 2n n=1

A: According to question,Given series,∑n=1+∞-1nnnsinn1n2n

Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: ー49 a+ 22ト7 40 +3)Y-(sin 32) (Cos 2) +e

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Q: 22. If y = (1- sin?x)i then y" is b. 1 COS X 2° а. C. - cos x d. -sin x sin x HIN HIN

A: The second derivative of the given function is solved in detail below.

Q: 10. Evaluate. (d) sin-1() (e) sin¬1 (sin (7)) (f) sin- (cos (E) (a) sin-' (0) (b) cos-1 (-) (c)…

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Q: 21. The general solution of 2 cos2 x – sin a -2 =0 is of the form x = An, b + 2nn, +2rn, n EI. The…

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Σ (-1)" (2n + 1)! Given: sin x = ,2п+1 for x E R n=0 (-1)"(2n + 1) Compute the exact value of the…

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Q: cos √x+1 O Σ n=2 (-1)"x²" (2n)! n+1 x² Σ nal

A: I have given the answer in the next step. Hope you understand that

Q: (1) Evaluate xdx Hint: Express cos* x in terms of sin x. Then use the substitution u = sin x. Back…

A: topic - indefinite integral

Q: |(4e" + 4x + 7 cos a + 2)dæ =, O et – x4 + cos a + 2+c - O 4e? + x4 + 7 cos x + 2x + c O 4e? + x4 –…

A: We have to find value of given Integral.

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

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Q: -1 -2<x< - 1 0 -1<x<1 1<x<2 nswer: f(x) = a + Tin COS ... COS n=1 sin T²n² O sin () COS

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Q: SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п <x< 8п n=1 +

A: The Fourier series of the function fx on -L,L is as follows. fx=a0+∑n=1∞ancosnπxL+bnsinnπxL. Use the…

Q: (-1)" (2n+1)! n=0 Σ Given: sin x x² n2n+1 for x E R (-1)"(2n +1) 4" (2n + 1)! Compute the exact…

A: Given: sinx=∑n=0∞-1n2n+1!x2n+1 for x∈ℝTo compute: The sum ∑n=0∞-1n2n+14n2n+1!

Q: 72 In x i. x(7ln a +1) – sin x - ii. xp: cos? x – 2 V6 cos x Cos2 - -

A: Integration

Q: x4 Evaluate 4- xp: Select one: 1 O 6 sin -x (x²+6) /4-x² +c 4 1 n-1승+ (x+6x)v4-x2 +c 2 O -(12…

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Q: 5. * S sin(1 – x) (2 – cos(1 – x))* dx A C (2-sin(1-x)5 +C (2-sin(1-x)5 +C+ D. (2-cos(1-x)5 +C…

A: topic - indefinite integral

Q: find the following limit

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Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: (d) Derive the formula 1 + X 1 In 1 - x tanh-'(x)

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: 2tan x In (cos x) dx= A sin x [In(cos x)] + c cos x [In(cos x)] + C © -[In(cos x)]? +C D [In(sinx)]?…

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Q: now that cos(ak – a/2) 2 sin(a/2) E sin(ak) : (1 %3D Taking the difference of cos(ak), A cos(ak) =…

A: We have to solve given problem:

Q: 3. The coefficients of the half-range sine expansion of the given function f (x) = 3 sin 2nx, for…

A: To find the coefficients of the half-range sine expansion of the below function for 0&lt;x&lt;1.…

Q: A violin string produces a vibration u(x,t)=a sin(2t-x/ 137). cos(A-t)+b sin(14t-x / 137). cos(E-t)…

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Q: 5√2 x Evaluate the integral ² cos ²0+2²) r do dr dz. 000 The value is (Type an exact answer, using x…

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Q: A s(1) = e-7" sin(8 1) () = e" sin(3 1) © s(1) = e3 sin(7 1) Os() = e-5 cos(71) D

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