\[\operatorname{gd}\left(x\right)=2\operatorname{arctan}\left(e^{x}\right)-%
\tfrac{1}{2}\pi\\
=\operatorname{arcsin}\left(\tanh x\right)=\operatorname{arccsc}\left(\coth x%
\right)\\
=\operatorname{arccos}\left(\operatorname{sech}x\right)=\operatorname{arcsec}%
\left(\cosh x\right)\\
=\operatorname{arctan}\left(\sinh x\right)=\operatorname{arccot}\left(%
\operatorname{csch}x\right).\]