Решение1) cos²t /(1 - sint) - sin²t - cos²t = sintУпростим левую часть тождества:cos²t / (1 - sint) - (sin²t + cos²t) = (cos²t - 1 + sint)/(1 - sint) = (- sin²t + sint)/(1 - sint) = [sint*(1 - sint)] / (1 - sint) = sintsint = sintдоказано2) tgt = 7/24 π < t < 3π/2 III четвертьtg²t + 1 = 1/cos²t, t ≠ π/2 + πk, k∈ Zcos²t = 1 / (tg²t + 1)cos²t = 1 / [(7/24)² + 1]cos²t = 1 / ( 49/576 + 1)cos²t = 576 / (625)cosx = - √(576/625) = - 24/25sinx = - √(1 - cos²t) = - √(1 - (-24/25)²) = √ (1 - 576/625) == - √(49/625) = - 7/25ctgt = 1 / tgt = 24/7