Cos^2t-ctg^2t/sin^2t-tg^2t

(cos²t - cos²t/sin²t) / (sin²t - sin²t/cos²t) = cos²t (sin²t-1) / sin²t : sin²t (cos²t-1) / cos²t=

=-cos^4t/sin²t : - sin^4t/cos²t=cos^4t/sin²t * cos²t/sin^4t=cos^6t/sin^6t=ctg^6t

Скобки на месте ставить надо. Скорее всего вид задания таков:

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

cos^2t-ctg^2t=cos^2t-cos^2t/sin^2t = (cos^2t*sin^2t-cos^2t) / sin^2t=

= (-cos^2t (1-sin^2t)) / sin^2t=-cos^4t/sin^2t - числитель

sin^2t-tg^2t=sin^2t-sin^2t/cos^2t = (sin^2t*cos^2t-sin^2t) / cos^2t=

= (-sin^2t (1-cos^2t)) / cos^2t=-sin^4t/cos^2t - знаменатель

Делим числитель на знаменатель

-cos^4t/sin^2t: (-sin^4t/cos^2t) = cos^6t/sin^6t=ctg^6t