Thread: Hyperbolic function..

Hi, I'm struggling with proof for this hyperbolic function, I just need a bit of explination if someone can help??

Let y=arccosh(x), then x=coshy
x = (e^y+e^-y)/2
2x = e^y+e^-y
e^(2y)-2xe^y+1 = 0
e^y = [2x +/- sqrt(4x^2-4)]/2

For the next step I understand it to be..
e^y = x +/- sqrt(2x^2-2)

but apparentley the correct answer is
e^y = x +/- sqrt(x^2-1)

How is this? surely your only dividing by 2... can someone please explain where I'm going wrong

Thanks..

Heres the rest, but i get that...

y = ln[x +/- sqrt(x^2-1)]
arccosh(x)=ln[x +/- sqrt(x^2-1)]

What were the instructions? What are you supposed to be doing with the "Let y =" bit?

Thank you!

I'm trying to prove that arccosh(x)=ln[x +/- sqrt(x^2-1)]...

Its the formulae for the inverse hyperbolic function arccos(x)