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

Replace $\left(1 - {\cos}^{2} x\right)$ by ${\sin}^{2} x$ and ${\cos}^{2} x$ by $1 - {\sin}^{2} x$, we get:
$\left(1 - {\cos}^{2} x\right) \left(1 + {\cos}^{2} x\right)$ =
${\sin}^{2} x \left(1 + 1 - {\sin}^{2} x\right)$=
${\sin}^{2} x \left(2 - {\sin}^{2} x\right) = 2 {\sin}^{2} x - {\sin}^{4} x$