Cosine of Sum/Proof 3

Theorem

 * $ \cos \left({a + b}\right) = \cos a \cos b - \sin a \sin b $

where $\sin$ denotes the sine and $\cos$ denotes the cosine.

Proof
Recall the Cosine Exponential Formulation:


 * $ \displaystyle \cos x = \frac 1 2 \left({ e^{-ix} + e^{ix} }\right) $

Then, starting from the RHS: