Pythagorean identity for coth and csch

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.18$