= (tan^2 a + sin^2 a) - sec^2 a
= tan^2 a + sin^2 a - sec^2 a
= (sin^2 a/cos^2 a + sin^2 a) - (1/cos^2 a)
= sin^2 a (1 + 1/cos^2 a) - 1/cos^2 a
= sin^2 a (cos^2 a + 1)/cos^2 a - 1/cos^2 a
= sin^2 a/cos^2 a - 1/cos^2 a
= (sin^2 a - 1)/cos^2 a