Product-to-Sum Identities

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