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Math Help - Proving an identity.

  1. #1
    Junior Member
    Joined
    Jan 2010
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    66

    Proving an identity.

    Hey guys!

    I'm stuck on a proof:

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

    I hate to be the kind of person who just dumps a problem on a forum without any work done, but proofs are kind of a special thing. It's like either you know where to start, or you don't.

    In this case, I don't!

    Thanks for any help.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    Hi

    \frac{\sin x}{1-\cot x}-\frac{\cos x}{\tan x - 1} = \frac{\sin x}{1-\frac{\cos x}{\sin x}}-\frac{\cos x}{\frac{\sin x}{\cos x} - 1} = \frac{\sin^2 x}{\sin x - \cos x}-\frac{\cos^2 x}{\sin x - \cos x}

    \frac{\sin x}{1-\cot x}-\frac{\cos x}{\tan x - 1} = \frac{\sin^2 x - \cos^2 x}{\sin x - \cos x} = \sin x + \cos x
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  3. #3
    Junior Member
    Joined
    Jan 2010
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    Thank you, running-gag!
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