Cotangent in terms of Hyperbolic Cotangent

Theorem
Let $z \in \C$ be a complex number.

Then:


 * $i \cot z = -\coth \paren {i z}$

where:
 * $\cot$ denotes the cotangent function
 * $\coth$ denotes the hyperbolic cotangent
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

 * Sine in terms of Hyperbolic Sine
 * Cosine in terms of Hyperbolic Cosine
 * Tangent in terms of Hyperbolic Tangent
 * Secant in terms of Hyperbolic Secant
 * Cosecant in terms of Hyperbolic Cosecant