Cotangent Exponential Formulation/Proof 2

Theorem
Let $z$ be a complex number.

Let $\tan z$ denote the cotangent function and $i$ denote the imaginary unit: $i^2 = -1$.

Then:


 * $\cot z = i \dfrac {e^{i z} + e^{-i z}} {e^{i z} - e^{-i z}}$