Difference between revisions of "Halving identity for tangent (2)"
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Latest revision as of 22:49, 21 October 2017
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.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.30$
