1) 60° это π/3; 144° - это 144·π/180 = 4π/5; 3π/4 - это 135°; 5π/18 - это 50°
2) Сos a = 2/√5
Sin²a + Cos² a = 1
Sin²a + 4/5 = 1
Sin² a = 1/5
Sin a = 1/√5
tg a = Sin a/Cos a = 1/√5 : 2/√5 = 1/2
3) Sin²t/(1 + Cos t) + Sin t·Cos t/Sin t =Sin²t/(1 + Cos t) + Cos t =
= (Sin²t + Cos t + Cos²t)/(1 + Cos t) = (1 + Cos t)/(1 + Cos t) = 1
4) Ctg t = -21/20 ⇒ tg t = -20/21
1 + tg² t = 1/Cos² t
1 + 400/441 = 1/Cos²t
841/441 = 1/Cos²t
Cos²t = 441/841
Сos t = 21/29
Sin² t + Cos²t = 1
441/841 + Cos²t = 1
Cos²t = 1 - 441/841= 400/841
Cos t = - 20/29