Question

Verify the identity:

cos4x=1-8cos^2x+8cos^4x

Answer 1

Recall some useful identities:
\[\cos2x=\cos^2x-\sin^2x~~\implies~~\cos4x=\cos^22x-\sin^22x\]
It'll also help to know that
\[\sin^2x=1-\cos^2x\]