Cos Trig Identity: Deriving Formula for Circuits Analysis

[paulmdrdo1]

Hello. Do you guys know if there is an identity related to this expression

$$\cos(A+B)\cos(A+C)$$

If so, can you help me how to derive it? I need it for the derivation of the formula from my circuits analysis course. Thanks.

 

[Ackbach]

Apparently, you can change it from a product to a sum like this:
$$\cos(A+B) \, \cos(A+C) = \frac12 \left[ \cos(2A + B + C) + \cos(B-C) \right].$$
Does that help?