# Halving identity for tangent (3)

From specialfunctionswiki

## 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.

## Proof

## References

- 1964: Milton Abramowitz and Irene A. Stegun:
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