Halving identity for tangent (2)

Theorem

The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \dfrac{\cosh(z)-1}{\sinh(z)},$$ where $\tanh$ denotes hyperbolic tangent, $\cosh$ denotes hyperbolic cosine, and $\sinh$ denotes hyperbolic sine.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.30$