hyperbolic functions – BAD MATHEMATICS

MitPY 12: Inverse Hyperbolic Functions

March 9, 2021

3:31 pm

This MitPY comes from occasional commenter, Craig:

Hello folks, just a quick (probably stupid) question. Is the following step justified?

$\boldsymbol{x = \ln\left(\cosh x + \sqrt{(\cosh x)^2-1}\right)}$

$\boldsymbol{\mbox{\bf arccosh}\, x = \ln\left(x+\sqrt{x^2 -1}\right)}$

Thanks.