Solve this: Question No 2The expression 8sin8x-cos8x can be expressed asA cos 2x + cos 6xB cos 2x +3 - Maths - Trigonometric Functions

Question

Solve this:
Question   No   2 The   expression   8 sin 8 x
- cos 8 x   can   be   expressed   as A  
cos   2 x   +   cos   6 x B   cos   2
x   + 3     cos   6 x C   - 7 cos 2 x
  +   cos   6 x D   2   sin 4   x
  cos 2   x - 1

Abhishek Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
consider,sin8x-cos8x=sin4x-cos4xsin4x+cos4x    ∵a2-b2=(a-b)(a+b)=sin2x-cos2xsin2x+cos2xsin2x2+cos2x2=sin2x-cos2x1sin2x+cos2x2-2cos2x sin2x      ∵a2+b2=(a+b)2-2ab and sin2A+cos2A=1=-cos2x1-2cos2x sin2x       ∵cos2A=cos2A-sin2A=cos2x2cos2x sin2x-1=cos2x(2sinx cosx)22-1=cos2xsin22x2-1     ∵sin2A=2sinA cosA=cos2x1-cos4x4-1     ∵cos2A=1-2sin2A=cos2x1-cos4x-44=-14cos2x3+cos4x=-143cos2x+cos2x cos4x=-143cos2x+cos2x+4x2+cos2x-4x22        ∵2cosAcosB=cos(A+B)+cos(A-B) and cos(-A)=cosA=-143cos2x+cos6x+cos2x2=-187cos2x+cos6xSo, 8sin8x-cos8x=-7cos2x+cos6x

Regards

Solve this: Question No . 2 The expression 8 sin 8 x - cos 8 x can be expressed as A cos 2 x + cos 6 x B cos 2 x + 3 cos 6 x C - 7 cos 2 x + cos 6 x D 2 sin 4 x cos 2 x - 1

Solve this:
$Question No . 2 The expression 8 (\sin^{8} x - \cos^{8} x) can be expressed as (A) \cos 2 x + \cos 6 x (B) \cos 2 x + 3 \cos 6 x (C) - (7 \cos 2 x + \cos 6 x) (D) 2 \sin^{4} x \cos^{2} x - 1$