Difference between revisions of "Halving identity for tangent (1)"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for cosh | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for cosh|next=Halving identity for tangent (2)}}: $4.5.30$ |
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[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 22:48, 21 October 2017
Theorem
The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \sqrt{ \dfrac{\cosh(z)-1}{2} },$$ where $\tanh$ denotes hyperbolic tangent and $\cosh$ denotes hyperbolic cosine.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.30$
