Question

(cos^2t - ctg^2t)/(sin^2t - tg^2t)

Answer 1

$frac{Cos^{2}t-Ctg^{2}t }{Sin{2}t-tg^{2}t}=frac{Cos^{2}t-frac{Cos^{2}t }{Sin^{2}t}}{Sin^{2}t-frac{Sin^{2}t }{Cos^{2}t }} =frac{frac{Sin^{2}tCos^{2}t-Cos^{2}t}{Sin^{2}t}}{frac{Sin^{2}tCos^{2}t-Sin^{2}t}{Cos^{2}t }}=frac{Cos^{2}t(Sin^{2}t-1)*Cos^{2}t }{Sin^{2}t(Cos^{2}t-1)*Sin^{2}t}=frac{-Cos^{2}t*Cos^{4}t}{-Sin^{2}t*Sin^{4}t}=frac{Cos^{6}t }{Sin^{6}t }=Ctg^{6}t$