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Math Help - Prove this is an Identity

  1. #1
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    Prove this is an Identity

    I am having trouble with this problem;
    \frac {tanx}{1-cotx}+\frac{cotx}{1-tanx}=1+secxcscx

    I have tired multiplying each fraction by the other denominator and have got stuck. I then tried to multiple each fraction by the its conjugate to get the identity but then I get stuck that way also. Then I tried the right side and got a common denominator then didn't know where to go form there.

    Thanks for the help. Its greatly appreciated.
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  2. #2
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    \displaystyle \frac{t}{1-1/t}+\frac{1/t}{1-t} = \frac{t^2}{t-1}+\frac{1}{t(1-t)} = \frac{t^3-1}{t(t-1)} = \frac{t^2+t+1}{t} =  1+t+\frac{1}{t}

    Therefore your LHS is equivalent to 1+\tan{x}+\cot{x}. So all that's left is to show that:

    ................................... \tan{x}+\cot{x} = \sec{x}\csc{x}.
    Last edited by TheCoffeeMachine; December 9th 2010 at 05:30 PM.
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