Sum to Product

The sum is added 2 trig functions together

Sine Identity

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

Cosine Identity

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