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Math Help - Trigonomeric identity

  1. #1
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    Talking Trigonomeric identity

    Hi does anybody now how to simplify this identity.
    "prove (Tanx/1-tanx)+(cosx/sin-cosx)=-1
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  2. #2
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    Quote Originally Posted by heatly View Post
    Hi does anybody now how to simplify this identity.
    "prove (Tanx/1-tanx)+(cosx/sin-cosx)=-1
    use,

    \tan x = \frac{\sin x}{\cos x}

    Spoiler:
    \frac{\tan x}{1-\tan x}+\frac{\cos x}{\sin x-\cos x}

    =\frac{\frac{\sin x}{\cos x}}{1-\frac{\sin x}{\cos x}}+\frac{\cos x}{\sin x-\cos x}

    =\frac{\sin x}{\cos x-\sin x}+\frac{\cos x}{\sin x-\cos x}

    =\frac{-\sin x}{\sin x-\cos x}+\frac{\cos x}{\sin x-\cos x}

    =\frac{-\sin x+\cos x}{\sin x-\cos x}

    =\frac{-(\sin x -\cos x)}{\sin x-\cos x}

    =-1
    Last edited by mr fantastic; June 26th 2009 at 03:44 AM.
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