SOLUTION: I need to prove this identity, working only one side. I have tried and tried but this one just won’t click with me!! {{{(1+cot^2x)(1-cos2x) = 2}}} Thanks

Algebra ->  Trigonometry-basics -> SOLUTION: I need to prove this identity, working only one side. I have tried and tried but this one just won’t click with me!! {{{(1+cot^2x)(1-cos2x) = 2}}} Thanks      Log On


   

Question 63545: I need to prove this identity, working only one side.
I have tried and tried but this one just won’t click with me!!
%281%2Bcot%5E2x%29%281-cos2x%29+=+2
Thanks
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2Bcot%5E2x%29%281-cos2x%29+=+2
There are two identities you need to solve this:
(1) sin^2x+cos^2x=1
(2) cos2x=1-2sin^2x
Remember that cotx = 1/tanx = 1/(sinx/cosx) = cosx/sinx.
Then, 1+cot^2x = 1+(cos^2x/sin^2x).
Turn 1 into cos^2x/cos^2x then 1+(cos^2x/sin^2x) becomes (cos^2x+sin^2x)/sin^2x = 1/sin^2x.
So, 1+cot^2x = 1/sin^2x.
Now, 1-cos2x = 1-(1-2sin^2x) = 2sin^2x.
So, (1+cot^2x)(1-cos2x) = (1/sin^2x)(2sin^2x) = 2 which is what we were trying to prove.
Make sense?