Express the following as a product of factors (1) sin 2x+sin6x +sin 8x (11) cos 54+ 2cos3.4+cos.4

Q: s nip

A: Given: 12cos2x+C=14cos2x

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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

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A: We need to verify the identity.

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Q: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

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

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A: Using Laplace transform,

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

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Q: Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

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Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

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Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

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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

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Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

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Q: Evaluate the integral : sin 60 do 2+ cos 60 using the substitution u = 2+ cos 60. sin 60 do = +C 2+…

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Q: The suitable substitution to evaluate sin24(x+2) dx is None 1 [1- cos4 (r+2)] [1+ cos8(r + 2)]…

A: Topic- integration

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

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Q: 4. Prove that cos(sin¬1 x) = /1 – x².

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Q: Express the following product as a sum. 2 cos(9x) sin(3x)

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Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

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

A: Solved below.

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

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Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

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Q: what is the integral of cos(6x)xsin(sin(6x)) from 0 to pi/12

A: Given,

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Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

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Q: 5) Determine the following indefinite integral cos (3x) (1 – sin(3x))(2 – sin(3x)) -dx

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Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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

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Q: Prove the following identities and show complete solution 1 Cos 8x - sin²2x + cos²2x %3D 8.

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Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the…

Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

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Q: How do you solve this and can you show me step by step?

A: Simplify the equation to get a quadratic in cos x.

Q: O Find the solutions of : 1+sinx=2(cosx)´ in the interval 0<x<2T.

A: