1. ## Proof hyperbolic equation

Show that $coth(x)+csc(x) = \frac{(1+e^-^1)^2}{1-(e^-^x)^2}$.

$\frac{coshx}{sinhx}+\frac{1}{sinhx}$

$\frac{e^x+e^-^x+2}{e^x-e^-^x}$

Can't understand how to approach from here.

2. ## Re: Proof hyperbolic equation

Hello, freestar!

There is a typo in the first equation . . .

. - - . . . . . . . . . . . . . . . . . . . . . . . . .
Show that: . $\coth(x)+\csch(x) \:=\: \frac{(1+e^{-1})^2}{1-(e^{-x})^2}$.

$\frac{\cosh x}{\sinh x}+\frac{1}{\sinh x} \;=\;\frac{e^x+e^{-x}+2}{e^x-e^{-x}}$

Can't understand how to approach from here.

We have: . $\frac{e^x + 2 + e^{- x}}{e^x-e^{-x}}$

Divide numerator and denominator by $e^x\!:$

. . $\frac{1 + 2e^{-x} + e^{-2x}}{1-e^{-2x}} \;=\; \frac{(1-e^{-x})^2}{1 - (e^{-x})^2}$