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Homework Help: 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
    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).
     
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