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Math Help - Double angle Prove question

  1. #1
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    Double angle Prove question

    Prove that:
    sin(2x)
    ---=cot(x)
    1-cos(2x)

    I've worked it down to simply cosx on the left side, but the other side is very annoying and confusing.
    Last edited by mr fantastic; May 14th 2010 at 08:35 PM.
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  2. #2
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    Hello, tallguywhoplaysguitar!

    We need some double-angle identities:

    . . \sin2x \;=\;2\sin x\cos x

    . . \sin^2\!x \:=\:\frac{1-\cos2x}{2} \quad\Rightarrow\quad 1 - \cos2x \:=\:2\sin^2\!x


    Prove that: . \frac{\sin2x}{1-\cos2x} \:=\:{\color{red}\cot x}


    We have: . \frac{\sin2x}{1-\cos2x}\;\;\begin{array}{c}\to \\ \to \end{array} \;\; \frac{2\sin x\cos x}{2\sin^2\!x} \;\;=\;\;\frac{\cos x}{\sin x} \;\;=\;\;\cot x

    Last edited by mr fantastic; May 14th 2010 at 08:34 PM.
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  3. #3
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    Smile

    thank you
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