Question

Помогите упростить выражение:с Ответ полный!

Answer 1

$cos^2t-(ctg^2t+1)cdot sin^2t=cos^2t-frac{cos^2t}{sin^2t}cdot sin^2t-sin^2t=\\=cos^2t-cos^2t-sin^2t=-sin^2t\\ frac{sin^2t-1}{cos^2t-1} +tgtcdot ctgt=frac{-cos^2t}{-sin^2t}+1=ctg^2t+1=frac{1}{sin^2t}$

Answer 2

cos^2t - (ctg^2t-1)*sin^2t=cos^2t - (cos^2t/sin^2t-1)*sin^2t= cos^2t - (cos^2t+sin^2t) =cos^2t - 1= - sin^2t.
(sin^2t-1)/(cos^2t-1)+tgt*ctgt = -cos^2t/(-sin^2t)+1= cos^2t/sin^2t+1=  (cos^2t+sin^2t)/sin^2t = 1/sin^2t.