Thread: 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?

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 ?

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.

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!