Question

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

Answer 1

\[\tanh(x)=\frac{\sinh(x)}{\cosh(x)}\rightarrow \sinh(x)=\cosh(x)\tanh(x)\]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\[\cosh(x)=\sqrt{\frac{1}{1-\tanh^2(x)}}=\sqrt{\frac{1}{1-(5/13)^2}}\]and you can finish it...except put plus or minus outside the sqrt (I didn't).

Answer 2

THANK U!