Prove that the $\displaystyle sinh^{-1}x = ln(x+\sqrt{x^{2}+1}) $

is $\displaystyle sinh^{-1}x = \frac{1}{sinhx} $ ?

if so than could I write

$\displaystyle sinh^{-1}x = \frac{2}{e^{x}-e^{-x}} $

and am not sure how to got from there, any help appreciated.