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Math Help - Help proving an identity

  1. #1
    Newbie
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    Apr 2010
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    Help proving an identity

    I have the identity (tanx/(1-cotx)) + (cotx/(1-tanx)) = 1 + tanx + cotx

    I have started by turning everything into tan, but from there i can't figure it out. Any help would be much appreciated, thank you.
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Hi and welcome to the forums

    Quote Originally Posted by masterkale View Post
    I have the identity (tanx/(1-cotx)) + (cotx/(1-tanx)) = 1 + tanx + cotx

    I have started by turning everything into tan, but from there i can't figure it out. Any help would be much appreciated, thank you.
    I think this is pretty basic, so

    (by the way I'm going to use that tan(x) = \frac{1}{cot(x)} )

     \frac{tan}{1-cot} + \frac{cot}{1-tan}

     \frac{tan^2}{tan-1} + \frac{cot}{1-tan}

     -\frac{tan^2}{1-tan} + \frac{cot}{1-tan}

     \frac{cot - tan^2}{1-tan}

     \frac{1 - tan^3}{tan(1-tan)}

     \frac{(1 - tan)( 1 + tan +tan^2)}{tan(1-tan)}

     \frac{( 1 + tan +tan^2)}{tan}

    1 + tan + cot

    do you still have questions on that problem? Then let us know

    Rapha
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