how do i prove that this is an identity?

$\displaystyle \frac{tan^2\theta}{1+tan^2\theta}+\frac{cot^3\thet a}{1+cot^2\theta}=\frac{1-2sin^2\theta cos^2\theta}{sin\theta cos\theta}$

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- Jul 29th 2009, 09:28 AMcrosser43How to prove as an identity?
how do i prove that this is an identity?

$\displaystyle \frac{tan^2\theta}{1+tan^2\theta}+\frac{cot^3\thet a}{1+cot^2\theta}=\frac{1-2sin^2\theta cos^2\theta}{sin\theta cos\theta}$ - Jul 29th 2009, 10:23 AMstapel
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.... (Wink) - Jul 29th 2009, 11:20 AMcrosser43
ok but does $\displaystyle 1+cot\theta$ equal to $\displaystyle 1-2sin^2\theta cos^2\theta$ ?

- Jul 29th 2009, 11:44 AMe^(i*pi)