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Exponential form

  1. May 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that:
    [tex]sinh(3x)=3sinh(x)+4sinh^{3}(x)[/tex]

    2. The attempt at a solution
    I know that:
    [tex]sinh(3x)=0.5(e^{3x}-e^{-3x})[/tex]

    and:
    [tex]3sinh(x)=1.5(e^{x}-e^{-x})[/tex]

    But I have no idea how to rewrite [tex]4sinh^{3}(x)[/tex] in exponential form...
     
    Last edited: May 10, 2009
  2. jcsd
  3. May 10, 2009 #2
    [tex]sinh^{3}(x) = [0.5(e^{x}-e^{-x})]^3[/tex]
     
  4. May 10, 2009 #3
    Allright thanks, then I get:

    [tex]0.5e^{3x}-0.5e^{-3x}=2e^{x}-2e^{-x}[/tex]
    Though I have no idea how to continue with this equation...
     
  5. May 10, 2009 #4
    How exactly did you arrive at that? It works for me.
     
  6. May 10, 2009 #5
    I made a mistake.

    [tex]sinh^{3}(x) = 0.125[(e^{x}-e^{-x})]^3[/tex]

    This is not equal to:

    [tex]sinh^{3}(x) = 0.125(e^{3x}-e^{-3x})[/tex]

    right?
     
  7. May 10, 2009 #6
    Remember:

    [tex] (a - b)^3 = a^3 - 3 a^2 b + 3a b^2 - b^3[/tex]
     
  8. May 10, 2009 #7
    Off course, thanks a lot!
     
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