Question

If tanh(x) =5/13 , find the value of the hyperbolic function of cosh(x) ...?

Answer 1

`\tanh(x)=(\sinh(x))/(\cosh(x))\rightarrow \sinh(x)=\cosh(x)\tanh(x)`

Now,


`\cosh^2(x)-\sinh^2(x)=1`

so substituting for sinh(x):


`\cosh^2(x)-\cosh^2(x)\tanh^2(x)=1\rightarrow \cosh^2(x)(1-\tanh^2(x))=1`

which means


`\cosh(x)=\pm\sqrt{(1)/(1-\tanh^2(x))}=\pm\sqrt{(1)/(1-((5)/(13))^2)}=\pm\sqrt{(1)/(1-(25)/(169))}=\pm\sqrt{(1)/((144)/(169))}= \pm(13)/(12) \\ \\`