Pythagorean identity for tanh and sech

Theorem

The following formula holds: $$\mathrm{tanh}^2(z)+\mathrm{sech}^2(z)=1,$$ where $\mathrm{tanh}$ denotes the hyperbolic tangent and $\mathrm{sech}$ denotes the hyperbolic secant.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.17$