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Math Help - Prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx)

  1. #1
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    Prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx)

    1. The problem statement, all variables and given/known data

    I can't seem to figure out how to prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx).

    2. Relevant equations

    I believe I just need to do appropriate substitution using compound angle formulas, double angle formulas, etc...

    3. The attempt at a solution

    I got as far as this

    1 + cot^2x - 2(1/tanx)(1/sinx) + cot^2x = (1-cosx)/(1+cosx)

    Can anyone help me figure this out? Thanks in advance!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Random-Hero- View Post
    1. The problem statement, all variables and given/known data

    I can't seem to figure out how to prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx).

    2. Relevant equations

    I believe I just need to do appropriate substitution using compound angle formulas, double angle formulas, etc...

    3. The attempt at a solution

    I got as far as this

    1 + cot^2x - 2(1/tanx)(1/sinx) + cot^2x = (1-cosx)/(1+cosx)

    Can anyone help me figure this out? Thanks in advance!!
    note that the left side is \frac {(1 - \cos x)^2}{\sin^2 x} (change everything to sines and cosines and simplify)

    to change the right side into this expression, multiply by \frac {1 - \cos x}{1 - \cos x}
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