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

Question

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

Comments

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

Answer 1

(cos²t-ctg²t)/(sin²t-tg²t)=ctg⁶t

1. cos²t-ctg²t=cos²t-cos²t/sin²t=(cos²t*sin²t-cos²t)/sin²t=cos²t*(sin²t-1)/sin²t=cos²t*(-cos²t)/sin²t=-cos⁴t/sin²t

2. sin²t-tg²t=sin²t-sin²t/cos²t=(sin²t*cos²t-sin²t)/cos²t=sin²t*(cos²t-1)/cos²t=sin²t*(-sin²t)/cos²t=-sin⁴t/cos²t

3. (-cos⁴t/sin²t):(-sin⁴t/cos²t)=cos⁶t/sin⁶t=ctg⁶t