Sine Exponential Formulation/Proof 2

Theorem
For any complex number $x$:


 * $\sin x = \dfrac {e^{i x} - e^{-i x}}{2 i}$

where $\sin x$ is the sine and $i^2 = -1$.

Proof
Recall Euler's Formula:


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

Then, starting from the RHS: