Use the identities cos^2 x + sin^2 x =1

Question

and

cos2x=cos^2 x -sin^2 x

to show that

cos^4 x -sin^4 x = cos2x

Im not sure how, I can solve my problem with half angle identities but im not sure where to start with this.

Answer 1

use x^2-y^2 = (x+y)(x-y)

c^4-s^4 = (c^2+s^2)(c^2-s^2)
= 1 (c^2-s^2)
= c 2x