Verify the identity. cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x

Question

 I'm confused.  Thank you for your help.

Answer 1

Replace (LHS) cos 4x by cos (2x+2x) which becomes cos²2x - sin²(2x) which equals 1 - 2 sin²2x.

 

Replace(LHS) cos 2x by 1 - 2sin²x.

 

Proceed to the finish line!