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Hyperbolic function proof

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that:
    (1+tanhx)/(1-tanhx)=e^(2x)

    2. Relevant equations

    09368019eae4f200d4ed8e266bfa50dc.png

    3. The attempt at a solution

    I tried substituting tanhx for (e^x-e^(-x))/(e^x+e^(-x)) and for (e^(2x)-1)/(e^(2x)+1))

    But I really have no clue how to continue...
     
  2. jcsd
  3. Mar 15, 2009 #2

    tiny-tim

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    Hi Pietair! :smile:

    Hint : (1+tanhx)/(1-tanhx) = (1 + sinhx/coshx)/(1 - sinhx/coshx) = … ? :wink:
     
  4. Mar 15, 2009 #3
    Thanks for your answer but it still doesn't make sense.

    I don't know how to rewrite it to something more "common".
     
  5. Mar 15, 2009 #4

    tiny-tim

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    try simplifying (1 + sinhx/coshx)/(1 - sinhx/coshx) …

    get rid of the internal fractions :wink:
     
  6. Mar 15, 2009 #5
    (coshx+sinhx)/(coshx-sinhx)

    = (0.5e^x+0.5e^(-x)+0.5e^x-0.5e^(-x))/((0.5e^x+0.5e^(-x)-0.5e^x+0.5e^(-x))

    = e^x/e^(-x)

    = e^2x (proven)

    Thanks a lot!
     
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