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)]