1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hyperbolic function proof

  1. Dec 2, 2003 #1
    I need help proving this hyperbolic function

    Prove that

    [tex]\tan^{-1}\hbar {x}=\frac{1}{2}\ln\frac{1+x}{1-x}[/tex]

    my work
    x=e^y-e^-y/e^y+e^-y
    (e^y+e^-y)x=e^y-e^-y

    0=e^y-e^-y-xe^y+xe^-y

    e^y(e^y-e^-y-xe^y+xe^-y)

    e^2y-x(e^2y)-1+x=0

    I know i have to use the quadratic equation here
     
    Last edited: Dec 2, 2003
  2. jcsd
  3. Dec 3, 2003 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    One problem you have is that you have "lost" a sign:

    instead of e^2y-x(e^2y)-1+x=0, the correct equation is
    e^(2y)- x(e^(2y))-1-x= 0 or, more simply, e^(2y)(1-x)= 1+x
    so e^(2y)= (1+x)/(1-x).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Hyperbolic function proof
  1. Hyperbolic functions (Replies: 1)

  2. Hyperbolic functions (Replies: 44)

Loading...