Posted by Haley on Wednesday, March 14, 2012 at 11:30pm.
I'll use x for theta, for my convenience.
(cos^4x - sin^4x)/sin^2x cos^2x
= (cos^2x - sin^2x)(cos^2x + sin^2x)/sin^2x cos^2x
= (cos^2x - sin^2x)/sin^2x * (cos^2x + sin^2x)/cos^2x
= (cot^2x - 1)(1+tan^2x)
= cot^2x - 1 + cot^2xtan^2x - tan^2x
= cot^2x - 1 + 1 - tan^2x
= cot^2x - tan^2x