Sum of Squares of Hyperbolic Secant and Tangent

Theorem

 * $\operatorname{sech}^2 x + \tanh^2 x = 1$

where $\operatorname{sech}$ and $\tanh$ are hyperbolic secant and hyperbolic tangent.

Also defined as
This result can also be reported as:
 * $1 - \tanh^2 x = \operatorname{sech}^2 x$

or:
 * $1 - \operatorname{sech}^2 x = \tanh^2 x$

Also see

 * Difference of Squares of Hyperbolic Cotangent and Cosecant