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Homework Help: Emergency ! A Half Angle Question. Please Help

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data
    How to verify this trigonometric equation? tanh z/2?
    verify that:

    tanh (z/2) = [sinh x + i sin y] / [cosh x + cos y]


    z is a complex number.

    How can i verify this equation?


    2. Relevant equations
    9957458708fa15c0a09a44ef7e3fbef8.png

    http://mathworld.wolfram.com/images/equations/HyperbolicTangent/Inline3.gif
    # sin(x + i y) = sin(x) cosh(y) + i cos(x) sinh(y).
    # cos(x + i y) = cos(x) cosh(y) - i sin(x) sinh(y).
    # tan(x + i y) = (tan(x) + i tanh(y)) / (1 - i tan(x) tanh(y)).
    # cot(x + i y) = (cot(x) coth(y) - i) / (i cot(x) + coth(y)).




    3. The attempt at a solution

    i have tried to solve from right hand side but it didn't work, then i have simplified the equation tanh(z/2) = e^z-1 / e^z+1


    if you help me, i will be appreciate.
    thanx a lot.
     
  2. jcsd
  3. Mar 14, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

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