Sine of Sum/Proof 3

Theorem

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

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

Proof
Recall the Sine Exponential Formulation:


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

Then, starting from the RHS: