Precalculus: Mathematics for Calculus, 7th Edition

$(\sin x+\cos x)^2=1+\sin 2x$
Start from the left side: $(\sin x+\cos x)^2$ Expand: $=\sin^2 x + 2\sin x\cos x+\cos^2 x$ Rearrange: $=\sin^2 x +\cos^2 x+ 2\sin x\cos x$ Use the identities $\sin^2 x +\cos^2 x=1$ and $2\sin x\cos x=\sin 2x$: $=1+ \sin 2x$ Since this is equal to the right side, the identity is proven.