
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^24)]/2
For the next step I understand it to be..
e^y = x +/ sqrt(2x^22)
but apparentley the correct answer is
e^y = x +/ sqrt(x^21)
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^21)]
arccosh(x)=ln[x +/ sqrt(x^21)]

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

I'm trying to prove that arccosh(x)=ln[x +/ sqrt(x^21)]...

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