Product-to-sum identities

The product-to-sum identities are as follows: sin(x)sin(y)=12(cos(xy)cos(x+y))sin(x)cos(y)=12(sin(xy)+sin(x+y))cos(x)cos(y)=12(cos(xy)+cos(x+y)) They can be derived by expanding out $\cos (x+y)$ and $\cos (x-y)$ or $\sin (x+y)$ and $\sin(x-y)$, then combining them to isolate each term.

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