Product-to-Sum Identities

1. Product of Sines

\sin A \sin B = \frac{1}{2} [\cos (A - B) - \cos (A + B)]

2. Product of Cosines

\cos A \cos B = \frac{1}{2} [\cos (A - B) + \cos (A + B)]

3. Product of Sine and Cosine

First Order:
$\sin A \cos B = \frac{1}{2} [\sin (A + B) + \sin (A - B)]$
Second Order:
$\cos A \sin B = \frac{1}{2} [\sin (A + B) - \sin (A - B)]$