Real Area Hyperbolic Cosine of Reciprocal equals Real Area Hyperbolic Secant

Theorem
Everywhere that the function is defined:
 * $\cosh^{-1} \left({\dfrac 1 x}\right) = \operatorname{sech}^{-1} x$

where $\sinh^{-1}$ and $\operatorname{csch}^{-1}$ denote inverse hyperbolic cosine and inverse hyperbolic secant respectively.