# Product-to-sum identities

The product-to-sum identities are as follows: \begin{align*} \sin (x) \sin (y) = \frac{1}{2} (\cos (x-y) - \cos (x+y)) \\ \sin (x) \cos (y) = \frac{1}{2} (\sin (x-y) + \sin (x+y)) \\ \cos (x) \cos (y) = \frac{1}{2} (\cos (x-y) + \cos (x+y)) \end{align*} They can be derived by expanding out and or and , then combining them to isolate each term.

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