Cosecant Exponential Formulation

Theorem
Let $z$ be a complex number.

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

Then:


 * $\csc z = \dfrac{2 i} {e^{i z} - e^{-i z} }$

Proof
{{eqn | l = \csc z     | r = \frac 1 {\sin z}      | c = {{{Defof|Complex Cosecant Function}} }}

Also see

 * Sine Exponential Formulation
 * Cosine Exponential Formulation
 * Tangent Exponential Formulation
 * Cotangent Exponential Formulation
 * Secant Exponential Formulation


 * Arccosecant Logarithmic Formulation