Answer
$(\sin x+\cos x)^2=1+\sin 2x$
Work Step by Step
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.