Question

Prove identity:

tan^2 (x) - sin^2 (x) =tan^2(x)sin^2(x)

Answer 1

use following identities:
tan^2 = sin^2/cos^2
sin^2 +cos^2 =1

sin^2/cos^2 - sin^2
= (sin^2 - sin^2cos^2)/cos^2
=sin^2(1-cos^2)/cos^2
=sin^2/cos^2 * (1-cos^2)
= tan^2*sin^2