Difference between revisions of "Halving identity for tangent (1)"

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(Created page with "==Theorem== The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \sqrt{ \dfrac{\cosh(z)-1}{2} },$$ where $\tanh$ denotes hyperbolic tangent and $\cosh$...")
 
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==References==
 
==References==
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for cosh|next=findme}}: $4.5.30$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for cosh|next=findme}}: $4.5.30$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for tangent (1)|next=Halving identity for tangent (2)}}: $4.5.30$
 
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Revision as of 22:47, 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