MHB Cos Trig Identity: Deriving Formula for Circuits Analysis

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The discussion focuses on deriving a cosine trigonometric identity for the expression cos(A+B)cos(A+C) relevant to circuit analysis. It is noted that this expression can be transformed into a sum using the identity cos(A+B)cos(A+C) = 1/2 [cos(2A + B + C) + cos(B-C)]. This transformation is crucial for simplifying calculations in circuit analysis. Participants seek clarification on the derivation process and its applications. Understanding this identity can enhance problem-solving in electrical engineering contexts.
paulmdrdo1
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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.
 
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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?
 

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