## Precalculus (6th Edition)

$(\cos 2x+\sin 2x)^2=1+\sin 4x$
Start with the left side: $(\cos 2x+\sin 2x)^2$ Expand: $=\cos^2 2x+2\cos 2x\sin 2x+\sin^2 2x$ Rearrange terms: $=\cos^2 2x+\sin^2 2x+2\cos 2x\sin 2x$ Use the identities $\cos^2 \theta+\sin^2\theta=1$ and $2\cos\theta\sin\theta=\sin 2\theta$, where $\theta=2x$: $=1+\sin (2*2x)$ $=1+\sin 4x$