Question

tan^2 theta - sin^2 theta = tan^2 theta.sin^2 theta​

Answer 1

$= {tan}^{2} \alpha - \sin {}^{2} ( \alpha ) \\ = \frac{ \sin {}^{2} ( \alpha ) - \sin {}^{2} ( \alpha ) \cos {}^{2} ( \alpha ) }{ \cos {}^{2} ( \alpha ) } \\ = \frac{ \sin {}^{2} ( \alpha )(1 - \cos {}^{2} ( \alpha ) }{ \cos {}^{2} ( \alpha ) } \\ = \frac{ \sin {}^{2} ( \alpha ) \times \sin {}^{2} ( \alpha ) }{ \cos {}^{2} ( \alpha ) } \\ = \tan {}^{2} ( \alpha ) \times \sin {}^{2} ( \alpha )$

hope it helps you