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


by Random-Hero-
Tags: 1cosx or 1, cosx, cotx2, cscx, prove
Random-Hero-
Random-Hero- is offline
#1
Feb10-09, 10:47 PM
P: 40
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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Dick
Dick is offline
#2
Feb10-09, 11:08 PM
Sci Advisor
HW Helper
Thanks
P: 25,160
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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