Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4 sin3θ

Q: Verify the identity: cos(α - β)/(cos α cos β) = 1 + tan α tan β.

A: We will use the identity

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

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Q: . Differentiate each function. a) y= cos'x b) y= sin(x³)

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Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: f(x) = (8 sin x + 3 cos x)tan1 -

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Q: If A = A-1 = 2e2t sin(5t) 2e²t cos(5t) 2e5t cos(5t) -2est sin(5t) , then 4

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Q: fip xp COS T 2. Oa) 2x sin(x) cos(2x) P-sin(2x) d- sin(x)+2x Osin(x) acer

A: y=cos (x2) We need to find dydx

Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

Q: cos( 2 sin1 (X/17)) = Select one: O 2x ( 289 - x )o./ 289 O ( 2x - 289 )/289 None O 34 x/( 289 + x)…

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Q: Is it true or false? cos(4x) - cos(3x) = cos(x) True False

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Q: Give the correct order for the following steps to show cos (0) (sec (0) + cos(0) csc²(0)) = csc²(0)

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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: 1. A. f sin 2x cos 5x dx B. f cos 2x cos 3x dx c. ftan³x sec5x dx

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Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

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Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: (cos A + sin A)/(cos A - sin A) = (1+ sin(2A))/ cos(2A)

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Q: If A A = = 3e³t sin(8t) 3e³t cos(8t) 3e²t cos(8t) -3e²¹ sin(8t) then

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

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Q: If csc(x)=8, for 90 degrees<(x)<180 degrees, then what is sine(x/20, cos(x/2), and tan(x/2)?

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Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: If () Z = tan || then 2z sin x 1+ z2

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Q: 1-) 2csc23x 1-S sec3xVsin3x

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Q: Compute | a° sin(æ" + 2) dæ.

A: Given : ∫x6sinx7+2dx