1) Verify the identity
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?
yes
(cos^2-sin^2)(cos^2+sin^2)
(cos^2-sin^2)(cos^2+(1-cos^2)
(cos2x)(1)
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?
(cos^2-sin^2)(cos^2+sin^2)
(cos^2-sin^2)(cos^2+(1-cos^2)
(cos2x)(1)