ctgt*tgt-(1+ctg²t)*sin²t=1-(1+cos²t/sin²t)*sin²t=1-((sin²t+cos²t)/sin²t))*sin²t=
=1-(1/sin²t)*sin²t=1-1=0.
ctgt*tgt-(1+ctg²t)*sin²t=1-(1+cos²t/sin²t)*sin²t=1-((sin²t+cos²t)/sin²t))*sin²t=
=1-(1/sin²t)*sin²t=1-1=0.