Question

как упрощать тригонометрическое выражение?
cos^2t-ctg^2t/sin^2-tg^2t
если можно по подробнее)

Answer 1

$frac{cos^2t-ctg^2t}{sin^2t-tg^2t}=frac{cos^2t-frac{cos^2t}{sin^2t}}{sin^2t-frac{sin^2t}{cos^2t}}=frac{(cos^2tcdot sin^2t-cos^2t)cdot cos^2t}{(sin^2tcdot cos^2t-sin^2t)cdot sin^2t}=\\=frac{cos^2tcdot (sin^2t-1)cdot cos^2t}{sin^2tcdot (cos^2t-1)cdot sin^2t}=frac{cos^2tcdot (-cos^2t)cdot cos^2t}{sin^2tcdot (-sin^2t)cdot sin^2t}=frac{cos^6t}{sin^6t} =ctg^6t$