Question 1058611

Please help me with the following question.

Prove this identity:

(1-cos^2x)(1+cos^2x) = 2sin^2x - sin^4x
<pre><b><u>LHS:</b></u>{{{(1 - cos^2 (x))(1 + cos^2 (x)) = 2 sin^2 (x) - sin^4 (x)}}}
{{{sin^2 (x)(1 + ( 1 - sin^2 (x)))}}} --- Replacing {{{matrix(2,3, 1 - cos^2 (x), with, sin^2 (x), cos^2 (x), with, 1 - sin^2 (x))}}} 
{{{sin^2 (x)(2 - sin^2 (x))}}}
{{{highlight_green(2sin^2 (x) - sin^4 (x))}}} ------- DISTRIBUTING (Same as RHS)