Pythagorean identity for coth and csch
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Theorem
The following formula holds: $$\mathrm{coth}^2(z)-\mathrm{csch}^2(z)=1,$$ where $\mathrm{coth}$ denotes hyperbolic cotangent and $\mathrm{csch}$ denotes hyperbolic cosecant.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.18$
