1) Verify the identity

Question

cos^4x - sin^4x = cos2x

I know that this is the difference of squares so (cos^2x)^2 - (sin^2x)^2 is this correct for the first step?

Answer 1

yes

(cos^2-sin^2)(cos^2+sin^2)
(cos^2-sin^2)(cos^2+(1-cos^2)
(cos2x)(1)