Answer
$\sinh x=\dfrac{12}{5} ;\\ \cosh x= \dfrac{3}{15} ;\\ \tanh x= \dfrac{12}{13} ; \\ sech x=\dfrac{5}{13} ; \\ csch x=\dfrac{5}{12} $ and $ coth x=\dfrac{13}{12}$
Work Step by Step
Given: $\cosh x=\dfrac{3}{15}$
The remaining hyperbolic functions can be found as follows:
Use the fact: $\cosh^2 x-\sinh^2x=1$
or, $(\dfrac{3}{15})^2-\sinh^2 x=1$ or, $ \sinh^2 x=\dfrac{144}{25}$
or, $\sinh x= \dfrac{12}{5}$
and $\tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{12}{5}}{\dfrac{3}{15}}=\dfrac{12}{13}$
Now, $sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{13}{5}}=\dfrac{5}{13}$
$csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{12}{5}}=\dfrac{5}{12}$
and $coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{12}{13}}=\dfrac{13}{12}$
