Упростите выражение

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

(cos²t-ctg²t) / (sin²t-tg²t) = (cos²t-cos²t/sin²t) / (sin²t-sin²t/cos²t) =

= (cos²t·sin²t-cos²t) ·cos²t/sin²t (cos²tsin²t-sin²t) =

=cos⁴t (sin²t-1) / sin⁴t (cos²t-1) = cos⁴t· (-cos²t) / sin⁴t· (-sin²t) = cos⁶t/sin⁶t=ctg⁶t;