Math — Sum-to-Product Identities

\sin A + \sin B = 2\sin\tfrac{A+B}{2}\cos\tfrac{A-B}{2}

\cos A + \cos B = 2\cos\tfrac{A+B}{2}\cos\tfrac{A-B}{2}

2\sin A\cos B = \sin(A+B) + \sin(A-B)

2\cos A\cos B = \cos(A+B) + \cos(A-B)