Question

Упростите выражение: sin²t·cos²t+sin⁴t / sin²t·cos²t+cos⁴t-1

Answer 1

sin²t·cos²t+sin⁴t / sin²t·cos²t+cos⁴t-1=sin²t(cos²t+sin²t)/[cos²t(sin²t+cos²t)-1]=
=sin²t/(cos²t-1)=sin²t/(-sin²t)=-1