Prove that

cos^2x-sin^2x/ctg^2x-tg^2x=sin^2x*cos^2x

First, notice that :

ctg^2x - tan^2x =    cos^2x/sin^2x - sin^2x/cos^2x  = [cos^4x - sin^4x]/[sin^2x cos^2x)..so we have..

[cos^2x - sin^2x] [sin^2xcos^2x]  / [cos^4x - sin^4x]  = 

[cos^2x - sin^2x] [sin^2xcos^2x] / [ (cos^2x - sin^2x) (cos^2x + sin^2x) ] =

[sin^2xcos^2x] / [sin^2x + cos^2x]              and [sin^2x + cos^2x ]  = 1  .....so....

sin^2xcos^2x  =  sin^2xcos^2x