hyper.tex

Definitions:
\vskip 3pt
\halign{\hfil$\displaystyle#$\hfil&$\displaystyle{} =#\quad$\hfil&$\quad\displaystyle#$\hfil&$\displaystyle{} = #$\hfil\cr
\sinh x  &{e^x - e^{-x} \over 2}, &\cosh x  &{e^x + e^{-x} \over 2},\cr
\tanh x  &{e^x - e^{-x} \over e^x + e^{-x}}, &\csch x &{1 \over \sinh x},\cr
\sech x &{1 \over \cosh x}, &\coth x &{1 \over \tanh x}.\cr
}

\vskip 8pt
\noindent Identities:
\vskip 8pt
\Dis 5pt
\baselineskip=20pt
\Fm \cosh^2 x - \sinh^2 x = 1, \Mf
\Fm \tanh^2 x + \sech^2 x = 1, \Mf
\Fm \coth^2 x - \csch^2 x = 1, \Mf
\Fm \sinh (-x) = - \sinh x, \Mf
\Fm \cosh (-x) = \cosh x, \Mf
\Fm \tanh (-x) = - \tanh x, \Mf
\Fm \sinh (x + y) = \sinh x \cosh y + \cosh x \sinh y, \Mf
\Fm \cosh (x + y) = \cosh x \cosh y + \sinh x \sinh y, \Mf
\Fm \sinh 2x = 2 \sinh x \cosh x, \Mf
\Fm \cosh 2x = \cosh^2 x + \sinh^2 x, \Mf
\Fm \cosh x + \sinh x = e^x, \Mf
\Fm \cosh x - \sinh x = e^{-x}, \Mf
\Fm (\cosh x + \sinh x)^n = \cosh n x + \sinh n x, \quad \hbox{$n \in \Z$}, \Mf
\Fm 2 \sinh^2 \sfrac x 2 = \cosh x - 1, \Mf
\Fm 2 \cosh^2 \sfrac x 2 = \cosh x + 1. \Mf
\EndDis