Answer
$\sinh x=\dfrac{8}{15}\\ \cosh x= \dfrac{17}{15}\\ \tanh x= \dfrac{8}{17} \\ sech x=\dfrac{15}{17} \\ csch x=\dfrac{15}{8} \\ coth x=\dfrac{17}{8}$
Work Step by Step
We are given: $\cosh x=\dfrac{17}{15}$
We need to find all the hyperbolic functions.
Use identity: $\cosh^2 x-\sinh^2x=1$
or, $(\dfrac{17}{15})^2-\sinh^2 x=1 \implies \sinh^2 x=\dfrac{64}{225}$ and $\sinh x= \dfrac{8}{15}$
Now, $\tanh x= \dfrac{\sin hx}{\cosh x}=\dfrac{\dfrac{8}{15}}{\dfrac{17}{15}}=\dfrac{8}{17}$
$sech x= \dfrac{1}{\cosh x}=\dfrac{1}{\dfrac{17}{15}}=\dfrac{15}{17}$;
$csch x= \dfrac{1}{\sinh x}=\dfrac{1}{\dfrac{8}{15}}=\dfrac{15}{8}$;
$coth x= \dfrac{1}{\tanh x}=\dfrac{1}{\dfrac{8}{17}}=\dfrac{17}{8}$