Product to Sum

Multiply 2 trigonometric functions together

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