Prove that ; cosec x . cosec 2x . sin 4x . cos 6x . cosec 10x cos 3x + cos 5x cos 7x cos 9x sin 2x sin 4x sin 4x sin 6x sin 6x sin 8x sin 8x sin 10x

Q: a) By expanding sin(2x+x) using double angle formulae, show that and sin 3x = 3 sin xr-4sin x.…

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Q: 63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x =…

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Q: d Select one: æ(sin=! æ)* 3x + 2 sin- x 3x x(sin x) -1 + 2(sin-1 x)? 1-a2 x² (sin-1 æ) 3(sin1 x) +…

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Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: Evaluate: Jcos 2xdx cos2x cos32х + C 6 A 2 sin2x sin32x + C 6 B 2

A:

Q: Express the product as a sum or difference. cos 4x cos 8x cos? 20x2 (cos 12x - cos 4x) (cos 12x -…

A: Express the product cos4x cos8x as a sum or difference

Q: Prove that the inequality|cos(x)|≥1−sin2(x) holds true for allx∈R

A: Given inequality is

Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

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Q: Evaluate: Jcos 2xdx cos2x, cos³2x + C 6 A + 2 cos 2x + C 6 cos2x B sin 2x + C 6 sin2x 2 sin2x sin32x…

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Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: Verify the following results  sin 4x = 8 cos3 x sin x − 4 cos x sin x

A: Given questions are two individual questions. So as per bartleby expert policy only one individual…

Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: Evaluate: /x?cos(2x)dx 2x2sin(2x) + 2xcos(2x) – sin(2 x) А + C 4 2x2sin(2x) – 2xcos(2x) – sin(2x) +C…

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Q: Using the Tabular method, not getting the same answer as my mathlab

A: To evaluate

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

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Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: Prove each of the following A. (sinx) (cotx+cosxtanx) =cosx+sin^2x B. (1-cosx)(1+cosx)/cos^2x=tan^2x

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Q: Use integral tables to evaluate sin (4x)dx. Choose the correct answer below. cos (4x) sin“(4x) + 3 4…

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Q: Evaluate the integral: 20 cos(20x+3) dx 23 sin (20x+3) Choose the most appropriate answer. Sin3 69…

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Q: Prove the following A. Secxtanx/tan^2x+1=sinx B.sin^2xcot^2x/1-sin^2x=1

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Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

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Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: 7. Suppose x is a number such that cos(x) = sin(x). Then: O a) cos(2x) = cos(x) O b) sin(2x) =…

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Q: Prove that X + 8 2 TT sin 8 2 1 sin x X sin?

A: We use Trigonometry identities , double angle formulas to prove this Question

Q: If 1, = |x" sin8x dx , Then 64 I,+n(n-1) I,-2 Select one: O- 8x" cos8x +n x" 7 sin8x O + 8x" cos8x…

A: Given :  In=∫xnsin8xdx                1 Using Integration by parts…

Q: 28. Evaluate f 5 sin 3x dx 2+cos 3x a. 2 In 15 sin 3x| + C b.- In 12+cos 3x|+C c. In 15 sin 3x| + C…

A: Evaluate integral

Q: Which of the following is true? A Jcos(3x)cos(4x)ax = [ cos(x) + cos(7x), 2 ® Jsin(3x)sin(4x)dx = […

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Q: Evaluate: tan( 4x- -In |cos (4x + 3)|+C B -In |sin(4x + 3)|+C -In |cse (4x + 3)|+C -In \sec (4x +…

A: the given integral,        ∫tan(4x+3) dx

Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: Use integral tables to evaluate sin (14x)dx. Choose the correct answer below. O A. cos (14x) sin…

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Q: Evaluate the integral. sin (8t + 9) -dt. cos (8t +9) sin (8t + 9) dt%3D cos (8t+ 9)

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Q: prove it 5. 2 sin (3x) = 1– cos(6x)

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Q: Evaluate f cos*x sin² xdx. 1 16 A B O A 1 -x+ sin 4x 48 1 =x+ 16 1 8 sin 4x 1 64 1 sin³ 2x + C sin³…

A: We need to evaluate integral.

Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

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Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: Evaluate: Jx?cos(2x)dx 2x2sin(2x) – 2xcos(2x) + sin(2x) A + C 4 2x?sin(2x) +2xcos(2x) – sin(2x) В +…

A:

Q: Evaluate: Jx°cos(2x)dx A None of the given choices 2x2sin(2x) +2xcos(2x) + sin(2x) + C 4…

A: I have used the by parts rule of integration and get the required integral . Option (D) is correct.

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: Suppose f(x) =cos ( 3x – 2). Evaluate: A -3sin(3x - 2)+C ® -sin(3x- 2) + C sin(3x – 2) +C 3sin( 3x –…

A: Given function f(x) = cos(3x-2)

Q: Prove that : A) sin(h3x) =3sin(hx)+4sin(h³ n(n°x) B) 13 cos(hx) 3 C) 2tan(hx) tan(h2x) 1+ tan(h²x)

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Q: Substitute the expressions for u and v in the integral. (글sin(| ») - / ÷a x cos 7x dx = sin( |x) dx…

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Q: Evaluate: cos32xdx cos³2x - +C 6. cos2x (A) cos32x +C cos2x B sin2x sin32x +C 6. = 2 sin32x + C 6.…

A: Given query is to find the integral.

Q: Evaluate (5x2+3) cos x dx O (5x2 + 1) sin x + 10x coSx – 10 sin x+C O (5x2 + 1) sin x – 10x coSx –…

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Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-