## Precalculus (6th Edition)

$\sin(x+y)+\sin(x-y)=2\sin x\cos y$
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.