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Math Help - Question regarding trig proof

  1. #1
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    Question regarding trig proof

    For some reason or another every time I come at this I get tangled:

    [1-cos(2x)] sin(4x)
    ________________ = tanx
    cos(2x) [1-cos(4x)]

    I have to prove it when {0,pi/2} and so x can't be 45 degree
    Last edited by mankauff; March 16th 2007 at 05:39 AM. Reason: I entered the problem in the wrong order
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  2. #2
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    Hello, mankauff!

    It's easy to get tangled in this problem . . .


    Prove, for 0 < x < π/2 and x ≠ π/4:

    sin(4x) [1 - cos(2x)]
    ------------------------ .= .tan(x)
    cos(2x) [1 - cos(4x)]

    I assume you know the necessary identities:
    . . sin2θ .= .2ĚsinθĚcosθ
    . . 1 - cos2θ .= .2Ěsin▓θ


    In the numerator: .sin(4x) .= .2Ěsin(2x)Ěcos(2x)
    . . . . . . . . . and: .1 - cos(2x) .= .2Ěsin▓(x)

    In the denominator: .1 - cos(4x) .= .2Ěsin▓(2x)


    . . . . . . . . . . . . . . . . . 2Ěsin(2x)Ěcos(2x) Ě 2Ěsin▓(x)
    The problem becomes: . --------------------------------
    . . . . . . . . . . . . . . . . . . . . cos(2x) Ě 2Ěsin▓(2x)


    . . . . . . . . . . . . . . . 2Ěsin▓(x). . . . . . 2Ěsin▓(x) . . . . . .sin(x)
    which simplifies to: . ---------- . = . ----------------- . = . ------- . = . tan(x)
    . . . . . . . . . . . . . . . .sin(2x) . . . . 2Ěsin(x)Ěcos(x) . - - .cos(x)

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  3. #3
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    It turns out that on about half an hour before you posted the answer, when I was playing around with the two identities that you checked to see if I knew, I ended up figuring it out on my own. But your explanation was still helpful! Thanks again!
    Last edited by mankauff; March 17th 2007 at 08:02 AM.
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