Answer
$\sinh x=\dfrac{8}{15}\\ \cosh x= \dfrac{17}{15} ;\\ \tanh x= \dfrac{8}{17} ;\\ sech x=\dfrac{15}{17}; \\ csch x=\dfrac{15}{8}$ and $ coth x=\dfrac{17}{8}$
Work Step by Step
Given: $\cosh x=\dfrac{17}{15}$
The remaining hyperbolic functions can be found as follows:
Use the fact:$\cosh^2 x-\sinh^2x=1$
or, $(\dfrac{17}{15})^2-\sinh^2 x=1 $ or, $ \sinh^2 x=\dfrac{64}{225}$
Thus, $\sinh x= \dfrac{8}{15}$
$\tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{8}{15}}{\dfrac{17}{15}}=\dfrac{8}{17}$
Now, $sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{17}{15}}=\dfrac{15}{17} \\ csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{8}{15}}=\dfrac{15}{8}$
and $coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{8}{17}}=\dfrac{17}{8}$
