# Relationship between csch, inverse Gudermannian, and cot

From specialfunctionswiki

** Theorem:** The following formula holds:
$$\mathrm{csch}(\mathrm{gd}^{-1}(x))=\cot(x),$$
where $\mathrm{csch}$ is the hyperbolic cosecant, $\mathrm{gd}^{-1}$ is the inverse Gudermannian, and $\cot$ is the cotangent.

**Proof:** █