# How do you verify (1-cos^2a)(1+cos^2a)=2sin^2a-sin^4a?

$L S = \left(1 - {\cos}^{2} a\right) \left(1 + {\cos}^{2} a\right) = {\sin}^{2} a \left(1 + {\cos}^{2} a\right) =$
$= {\sin}^{2} a + {\sin}^{2} a . {\cos}^{2} a = {\sin}^{2} a + {\sin}^{2} a \left(1 - {\sin}^{2} a\right) =$
$= 2 {\sin}^{2} a - {\sin}^{4} a$