establish this identity

• Oct 9th 2012, 05:03 PM
avatartiger2
establish this identity
(1+ cos^2 theta)(1- cot^2 theta)= 1

I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?
• Oct 9th 2012, 05:14 PM
skeeter
Re: establish this identity
Quote:

Originally Posted by avatartiger2
(1+ cos^2 theta)(1- cot^2 theta)= 1

I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?

you sure it's not $(1 - \cos^2{\theta})(1 + \cot^2{\theta}) = 1$ ?
• Oct 9th 2012, 05:24 PM
johnsomeone
Re: establish this identity
Idea: First, unpack cotangent in terms of sine and cosine. Then simplify (multiply out - or something even better if you see it) the left hand side.
Also, I believe that skeeter's correct about the actual problem intended.
• Oct 9th 2012, 05:50 PM
avatartiger2
Re: establish this identity
yeah! i looked over the problem and I think the textbook might have switched the signs! (1-cos^2 theta)(1+ cot^2 theta) does simplify to 1. I kept doing the other problem over and over again. thanks for telling me! what a relief!