Thread: 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!!

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 (change everything to sines and cosines and simplify)

to change the right side into this expression, multiply by