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

Question

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

Answer 1

(cos²t-ctg²t)/(sin²t-tg²t)=ctg⁶t

1. cos²t-ctg²t=cos²t-cos²t/sin²t=(cos²t *sin²t-cos²t)/sin²t=cos²t*(sin²t-1)/sin²t=-cos⁴t/sin²t
2. sin²t-tg²t=sin²t-sin²t/cos²t=(sin²t *cos²t-sin²t)/cos²t=sin²t*(cos²t-1)/cos²t=-sin⁴t/cos²t
3. (-cos⁴t/sin²t)/(-sin⁴t/cos²t)=cos⁶t/sin⁶t=ctg⁶t

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