Answer
$\displaystyle \sinh x=\frac{\sqrt{3}}{3}$
$\mathrm{c}\mathrm{s}\mathrm{c}\mathrm{h} x=\sqrt{3}$
$\displaystyle \cosh x=\frac{2\sqrt{3}}{3}$
$\displaystyle \mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}x=\frac{\sqrt{3}}{2}$
$\coth x=2$
Work Step by Step
$\begin{align*}
\tanh^{2}x+{\rm sech}^{2}x&=1\\
{\rm sech}^{2}x&=1-\tanh^{2}x \\
{\rm sech}^{2}x&=1-\displaystyle \frac{1}{4} \\\\
{\rm sech} x&=\sqrt{3/4} \\\\
& =\displaystyle \frac{\sqrt{3}}{2} \end{align*}$
$\displaystyle \mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}x=\frac{\sqrt{3}}{2}$
$\displaystyle \cosh x=\frac{1}{{\rm sech} x}=\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$
$\displaystyle \coth x=\frac{1}{\tanh x}=\frac{1}{1/2}=2$
$\displaystyle \sinh x=\tanh x\cosh x=\frac{1}{2}\cdot\frac{2\sqrt{3}}{3}=\frac{\sqrt{3}}{3}$
$\mathrm{c}\mathrm{s}\mathrm{c}\mathrm{h} x=\displaystyle \frac{1}{\sqrt{3}/3}=\sqrt{3}$
