Maths

Prove that: (sinx-2sin2x+sin3x)/(sinx+2sin2x+sin3x)= -tan^2 x/2.

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  1. sinx + sin3x = 4sinx cos^2x = 2sin2x cosx

    So, you have

    (2sin2x cosx - 2sin2x)
    ---------------------------
    (2sin2x cosx + 2sin2x)

    2sin2x(cosx-1)
    ---------------------
    2sin2x(cosx+1)

    = (cosx-1)/(cosx+1)

    Now take a look at the half-angle formula for tan(x/2)

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    posted by Steve
  2. I don't understand it....

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    posted by Mahlatse
  3. tan^2(x/2) = (1-cosx)/(1+cosx)

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    posted by Steve

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