#### Answer

$(\sin x+\cos x)^2=\sin 2x+1$

#### Work Step by Step

Start with the left side:
$(\sin x+\cos x)^2$
Expand:
$=\sin^2 x+2\sin x\cos x+\cos^2 x$
Rearrange terms:
$=2\sin x\cos x+(\sin^2 x+\cos^2 x)$
Use the identities $2\sin x\cos x=\sin 2x$ and $\sin^2 x+\cos^2 x=1$:
$=\sin 2x+1$
Since this equals the right side, the identity has been proven.