Tangent in terms of Hyperbolic Tangent

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

Then:


 * $i \tan z = \tanh \paren {i z}$

where:
 * $\tan$ denotes the tangent function
 * $\tanh$ denotes the hyperbolic tangent
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

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