math
posted by Haley on .
prove the identity :
cos^4 theta sin ^4 thetaover sin squared theta cos squared theta =cot squared theta  tan squared theta

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