Halving identity for tangent (3)

Theorem

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

References

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