Question

verify
cos^4 2theta + sin^2 2 theta = cos^2 2theta + sin^4 2 theta

Answer 1

\[\cos^4 2\theta + \sin^2 2\theta = (1-\sin^2 2\theta)^2 + \sin^2 2\theta\\\quad =1-2\sin^2 2\theta + (\sin^2 2\theta)^2+\sin^2\theta\\\quad = \dots\]