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Math Help - Proving (Q8B)

  1. #1
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    Proving (Q8B)

    Prove that \frac{2sin2x-sin4x}{2sin2x+sin4x}=tan^2x
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  2. #2
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    Quote Originally Posted by Punch View Post
    Prove that \frac{2sin2x-sin4x}{2sin2x+sin4x}=tan^2x
    sin 2x = 2 sin x cos x

    sin 4x = 2 sin 2x cos 2x

    Substitute this into the equation, factor whatever is necessary to simplify the expression and see where that leads you.
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  3. #3
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    2 sin(2x) = 4 sin(x)·cos(x)
    sin(4x) = 2 sin(2x)·cos(2x) = 4sin(x)·cos(x)·cos(2x)
    cos(2x) = cos(x)-sin(x)



    Ok, with that solved we can now begin.

    (2 sin(2x)-sin(4x))/(2sin(2x)+sin(4x)) =
    (4sin(x)·cos(x)-4sin(x)·cos(x)·cos(2x))/(4(sin(x)·cos(x)+4sin(x)·cos(x)·cos(2x) =
    (4sin(x)·cos(x)(1-cos(2x)))/(4sin(x)·cos(x)(1+cos(2x)) =
    (1-cos(2x))/(1+cos(2x)) =
    (1-(cos(x)-sin(x))/(1+cos(x)-sin(x)) =
    (sin(x)+cos(x)-cos(x)+sin(x))/(sin(x)+cos(x)+cos(x)-sin(x) =
    2sin(x)/2cos(x) = tan(x)
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