Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 667: 72

$\tan^2\alpha \sin ^{2}\alpha =\tan ^{2}\alpha +\cos ^{2}\alpha -1$

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