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Math Help - Hyperbolic Function Identities

  1. #1
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    Alberta
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    Hyperbolic Function Identities

    Hey, I'm having a hell of a time trying to figure out this simplification; If anyone has any input, it would be greatly appreciated!

    Show that:  \frac{sinh(3t)}{sinh(t)} = 1 + 2 cosh(2t) \ for \ t \neq 0
    I've tried breaking the  \frac{sinh(3t)}{sinh(t)} side down by turning it into \frac{sinh (2t+t)}{sinh t} and using the sinh (t+u) identity, but everything i do just seems to complicate the whole deal by expanding it to huge proportions that doesn't chop down any.

    Any ideas on a hot identity to try? I'm not sure how else to approach this.
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  2. #2
    MPK
    MPK is offline
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    Hello,

    try using : sh(3x) = 0.5 * (e^(3x) - e^(-3x))

    sh(x) = 0.5 * (e^(x) - e^(-x))

    sh(3x)/sh(x) = (e^(3x) - e^(-3x))/(e^(x) - e^(-x))

    and then use the fact that :

    a^3 -b^3 = (a-b)(aČ + ab + bČ)

    and it will be paradise not hell
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  3. #3
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    Oh man I never thought to break it down into exponentials!

    But I'm lost on how I can use a^3 - b^3 = (a-b)(a^2 - ab + b^2) with e^{3t} - e^{-3t} because of the negative exponent on the second e? Don't I have e^{3t} - \frac{1}{e^{3t}}?
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