Answer
$\sin(x+y)+\sin(x-y)=2\sin x\cos y$
Work Step by Step
Start with the left side:
$\sin(x+y)+\sin(x-y)$
Use the sum and difference formulas on page 673:
$=(\sin x\cos y+\cos x\sin y)+(\sin x\cos y-\cos x\sin y)$
$=\sin x\cos y+\cos x\sin y+\sin x\cos y-\cos x\sin y$
$=2\sin x\cos y$
Since this equals the right side, the identity has been proven.
