Something to keep you occupied - reposted

Note that $\sec(t) =\cosh(t) \Rightarrow \sec^2(t) = \cosh^2(t) \Rightarrow \sec^2(t)-1=\cosh^2(t)-1\Rightarrow \tan^2(t) = \sinh^2(t)\Rightarrow \tan(t)=\pm\sinh(t).$

By graphing the functions and zooming in on the points, I was able to tell that sometimes when $\sec(t)=\cosh(t),$ we have $\tanh(t)=\sinh(t).$ The other times $\sec(t)=\cosh(t)$ (when $\tan(t)\neq \sinh(t)$ ), we have $\tan(t)=-\sinh(t).$ Conversely, when we have $\tan(t)=\sinh(t),$ we either get $\sec(t)=\cosh(t)$ or $\sec(t)=-\cosh(t)$ , depending on the value of $t.$