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

  1. 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!!
  2. jcsd
  3. Dick

    Dick 25,910
    Science Advisor
    Homework Helper

    It's not that complicated. Turn everything into sin's and cos's. The denominator is sin(x)^2. That's (1-cos^2(x)). Factor it.
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