Question 591078
How can I prove this identity? (1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta?

I tried to do it, and this is what I've come up with so far, and am not sure if I am doing it correctly.

Working with the left side, I have the following:

sin^2theta(1+cos^2theta) = 

sin^2theta+(sin^2theta*cos^2theta)
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(1-cos^2theta)(1+cos^2theta)=2sin^2theta-sin^4theta?
sin^2(t)*(1+cos^2theta)=2sin^2theta - sin^4theta?
(1+cos^2theta) = 2 - sin^2theta?
1+cos^2theta + sin^(t) = 2
cos^2(t) + sin^(t) = 1
I'm convinced.