# How do you prove tan^2xsin^2x=tan^2x + cos^2x-1?

${\tan}^{2} x . {\sin}^{2} x = {\tan}^{2} x \left(1 - {\cos}^{2} x\right) = {\tan}^{2} x - {\tan}^{2} x \left({\cos}^{2} x\right)$
$= {\tan}^{2} x - \frac{{\sin}^{2} x . {\cos}^{2} x}{{\cos}^{2} x} = {\tan}^{2} x - {\sin}^{2} x =$
$= {\tan}^{2} x - 1 + {\cos}^{2} x$