# How to prove as an identity?

• July 29th 2009, 10:28 AM
crosser43
How to prove as an identity?
how do i prove that this is an identity?
$\frac{tan^2\theta}{1+tan^2\theta}+\frac{cot^3\thet a}{1+cot^2\theta}=\frac{1-2sin^2\theta cos^2\theta}{sin\theta cos\theta}$
• July 29th 2009, 11:23 AM
stapel
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)
• July 29th 2009, 12:20 PM
crosser43
ok but does $1+cot\theta$ equal to $1-2sin^2\theta cos^2\theta$ ?
• July 29th 2009, 12:44 PM
e^(i*pi)
Quote:

Originally Posted by crosser43
ok but does $1+cot\theta$ equal to $1-2sin^2\theta cos^2\theta$ ?

$
1+cot(x) = 1+\frac{cos(x)}{sin(x)} = \frac{cos(x)+sin(x)}{sin(x)}$

You may recall that $1+tan^2(x) = sec^2(x)$ and $1+cot^2(x) = csc^2(x)$