# Math Help - Identities Problem

1. ## Identities Problem

How someone help me prove the identity below?

(1-tan^2X)(1-cos^2X)=[(sin^2X-4sin^4X)/(1-sin^2X)]

2. Hello Hellooo

Welcome to Math Help Forum!
Originally Posted by Hellooo
How someone help me prove the identity below?

(1-tan^2X)(1-cos^2X)=[(sin^2X-4sin^4X)/(1-sin^2X)]

I think the 4 on the RHS should be a 2. Here's my answer:

$(1-\tan^2x)(1-\cos^2x)$
$=\left(1-\frac{\sin^2x}{\cos^2x}\right)\sin^2x$, using $\tan x = \frac{\sin x}{\cos x}$ and $1 - \cos^2x = \sin^2 x$

$=\frac{(\cos^2x-\sin^2x)\sin^2x}{\cos^2x}$

$=\frac{(1-2\sin^2x)\sin^2x}{1-\sin^2x}$, using $\cos^2x =1-\sin^2x$

$=\frac{\sin^2x-2\sin^4x}{1-\sin^2x}$