how do i prove that this is an identity?
$\displaystyle \frac{tan^2\theta}{1+tan^2\theta}+\frac{cot^3\thet a}{1+cot^2\theta}=\frac{1-2sin^2\theta cos^2\theta}{sin\theta cos\theta}$
The left-hand side, having two fractions, is (or at least looks to be) more complicated than the right-hand side, so try working on the left-hand side.
A good start would probably be to convert everything to sines and cosines, convert to a common denominator, combine the two fractions, and see where that leads....