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Math Help - Differentiation Question

  1. #1
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    Ardkeen
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    Differentiation Question

    Let y = 1 - cos x / 1 + cosx

    Show that dy/dx = t+t^3 , where t = tan(x/2)
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  2. #2
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    Re: Differentiation Question

    Probably easiest to get y in terms of half x right away, using

    \cos(2x) \equiv \cos^2 x - \sin^2 x

    i.e. \displaystyle{\cos(x) \equiv \cos^2 \frac{x}{2} - \sin^2 \frac{x}{2}\displaystyle{

    Then simplify using Pythag,

    \cos^2 x + \sin^2 x \equiv 1
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  3. #3
    MHF Contributor

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    Re: Differentiation Question

    Its it possible that you mean (1- cos(x))/(1+ cos(x))?
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