Cosine Exponential Formulation/Proof 2

Theorem
For any complex number $x$,


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

where $\cos x$ is the cosine and $i^2 = -1$.

Proof
Recall Euler's Formula:


 * $ \displaystyle e^{ix} = \cos x + i \sin x $

Then, starting from the RHS: