Question

Verify the identity.

cos 4x + cos 2x = 2 - 2 sin^2(2x) - 2 sin^2 x

Answer 1

using the identity
cos 2A = cos^2 A - sin^2 A = 1 - 2sin^2 x = 2cos^2 x -1

LS = cos 4x + cos 2x
= cos^2 2x - sin^2 2x + cos 2x
= (1 - sin^2 (2x) ) - sin^2 (2x) + (1 - 2sin^2 x)
= 1 - 2sin^2 (2x) + 1 - 2sin^2 x
= 2 - 2sin^2 (2x) - 2sin^2 x
= RS

Answer 2

Ok wtf was that