we will start with tan^2 theta - sin^2 theta
[tex]\tan ^2\text{ }\theta-sin^2\theta[/tex]
remember tan theta = sin theta / cos theta
[tex](\frac{\sin \theta}{\cos \theta})^2\text{ - }\sin ^2\theta[/tex][tex](\frac{\sin\theta}{\cos\theta})^2\text{ - }\sin ^2\theta\text{ }\ast\frac{\cos ^2\theta}{\cos ^2\theta}[/tex][tex]\frac{\sin ^2\theta(1-\cos ^2\theta)}{\cos ^2\theta}[/tex][tex]\tan ^2\theta\text{ (1 - }\cos ^2\theta\text{)}[/tex][tex]\tan ^2\theta\ast\sin ^2\theta[/tex]