Answer
$(\sin x+\cos x)^{2}=1+2\sin x\cos x$
Work Step by Step
$(\sin x+\cos x)^{2}=1+2\sin x\cos x$
Evaluate the power on the left side of the equation:
$\sin^{2}x+2\sin x\cos x+\cos^{2}x=2\sin x\cos x$
Since $\sin^{2}x+\cos^{2}x=1$, identity is proved:
$1+2\sin x\cos x=1+2\sin x\cos x$
