Упростить: а) (Cos квадрат t / 1 - sin(t)) - Sin(t) б) tg(t) / tg(t) + ctg(t) в) (...

Question

Упростить:
а) (Cos квадрат t / 1 - sin(t)) - Sin(t)
б) tg(t) / tg(t) + ctg(t)
в) ( (Sin(t) + Cos(t)) в квадрате - 1 ) / ctg(t) - Sin(t)*Cos(t)

Answer 1

1)(1-sin²t)/(1-sint)-sint=(1-sint)(1+sint)/(1-sint) -sint=1+sint-sint=1
2)sint/cost:(sint/cost+cost/sint)=sint/cost:(sin²t+cos²t0sintcost=
=sint/cost:1/sintcost=sint/cost * sintcost=sin²t
3)(sin²t+2sintcost+cos²t-sin²t-cos²t):(cost/sint -sintcost)=
=2sintcost : (cost-sin²tcost)/sint=2sintcost :cost(1-sin²t)/sint=
=2sintcost*sint/cos³t=2sin²t/cos²t=2tg²t