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

• Feb 10th 2009, 07:51 PM
Random-Hero-
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!!
• Feb 10th 2009, 08:02 PM
Jhevon
Quote:

Originally Posted by Random-Hero-
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 $\displaystyle \frac {(1 - \cos x)^2}{\sin^2 x}$ (change everything to sines and cosines and simplify)

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