Решение
1) cos²t /(1 - sint) - sin²t - cos²t = sint
Упростим левую часть тождества:
cos²t / (1 - sint) - (sin²t + cos²t) = (cos²t - 1 + sint)/(1 - sint) =
(- sin²t + sint)/(1 - sint) = [sint*(1 - sint)] / (1 - sint) = sint
sint = sint
доказано
2) tgt = 7/24 π < t < 3π/2 III четверть
tg²t + 1 = 1/cos²t, t ≠ π/2 + πk, k∈ Z
cos²t = 1 / (tg²t + 1)
cos²t = 1 / [(7/24)² + 1]
cos²t = 1 / ( 49/576 + 1)
cos²t = 576 / (625)
cosx = - √(576/625) = - 24/25
sinx = - √(1 - cos²t) = - √(1 - (-24/25)²) = √ (1 - 576/625) =
= - √(49/625) = - 7/25
ctgt = 1 / tgt = 24/7