Name of trigonometric identity

Question

Is there a name of this trigonometric identity: $$\cos(a+b) \cos(a+c+b) \equiv \frac{1}{2} \left[\cos(c) + \cos(2a+2b+c) \right]$$

Bsaically we are "changing" a product of cosines into a sum of cosines.

Answer 1

This is a result of angle sum and difference identities.

$\cos(a+b) = \cos(a)\cos(b)-\sin(a)\sin(b)$

$\cos(a-b) = \cos(a)\cos(b)+\sin(a)\sin(b)$

Therefore

$\cos(a)\cos(b) = \frac{1}{2}(\cos(a+b)+\cos(a-b))$