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
Heres the rest, but i get that...
y = ln[x +/- sqrt(x^2-1)]
arccosh(x)=ln[x +/- sqrt(x^2-1)]