Question

To prove cos4x.cosx+sin4x.sinx=cos2xcosx-sin2xsinx

Answer 1

Step-by-step explanation:

cos4x.cosx+sin4x.sinx=cos2xcosx-sin2xsinx

cos4x.cosx - cos2x cosx + sin4x.sinx + sin2x. sinx=0

cosx ( cos4x- cos2x) + sinx (sin4x + sin2x)=0

cosx [-2sin (4x+2x)/2 sin( 4x-2x)/2] + sinx [2sin(4x+2x)/2 cos(4x-2x)/2]. =0

- 2cosx sin3x sinx + 2sinx sin3x cosx =0

2sinx sin3x cosx = 2cosx sin 3x sin x

LHS = RHS