First show that tan^2(x)sin^2(x) = tan^2(x) - sin^2(x):

tan^2(x) - sin^2(x)
sin^2(x)/cos^2(x) - sin^2(x)
[sin^2(x) - cos^2(x)sin^2(x)]/cos^2(x)
sin^2(x)(1 - cos^2(x))/cos^2(x)
sin^2(x)sin^2(x)/cos^2(x)
tan^2(x)sin^2(x)

Now you can re-write the statement as tan^2(x)-(tan^2(x)-sin^2(x)) = sin^2(x)