Product-to-sum identities

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

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See Also

• Trigonometric identities