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Math Help - Prove this identity (quick!)

  1. #1
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    Prove this identity (quick!)

    Prove this identity:

    [ (cos x) / (1 - tan x) ] + [ (sin x) / (1 - cot x) ] = cos x + sin x

    So far I was able to put everything in terms of sin x and cos x
    I understand that you have to multiply each dominator and numerator to get the common dominator.
    Anyway, I got to this portion of it:

    [ (cos^2 x) / (cos - sin) ] + [ (sin^2 x) / (sin - cos) ] = cos x + sin x

    I do have a solution I could copy, but I'd rather understand how to do the problem. It's quite frustrating.
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  2. #2
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    Nov 2008
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    Quote Originally Posted by Skynt View Post
    Prove this identity:

    [ (cos x) / (1 - tan x) ] + [ (sin x) / (1 - cot x) ] = cos x + sin x

    So far I was able to put everything in terms of sin x and cos x
    I understand that you have to multiply each dominator and numerator to get the common dominator.
    Anyway, I got to this portion of it:

    [ (cos^2 x) / (cos - sin) ] + [ (sin^2 x) / (sin - cos) ] = cos x + sin x

    I do have a solution I could copy, but I'd rather understand how to do the problem. It's quite frustrating.
    ++++++++++++++++++++++++++++++++++++++++++++++++++ ++++
    Skynt,
    You are almost there.
    work little more on dominator then it will become
    ( sin^2x - cos^2x ) / ( sin x - cos x )

    and then
    [ (sin x + cos x) ( sin x - cos x) ] / ( sin x - cos x)

    and you start to cancel ( sin x - cos x ) at numinator and dominator. the only thing left is ( sin x + cos x )
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