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

1. anonymous

$\tanh(x)=\frac{\sinh(x)}{\cosh(x)}\rightarrow \sinh(x)=\cosh(x)\tanh(x)$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).

2. anonymous

THANK U!