1) ctg t cos t / sin t cos t / sin t
---------------- = --------------------------------- = -------------------------------------- =
tg t + ctg t sin t / cos t + cos t / sin t (sin²t + cos²t) / (sin t * cos t)
= (cos t / sin t) = sin t * cos t = cos²t
2) 2 * sin 870° + √ 12 * cos 570° - tg² 60° = 2 * sin (900°- 30°) + √ 12 * cos (540°+ 30°) - (√ 3)² = 2 * sin 30° - √ 12 * cos 30° - 3 = 2 * 0,5 - √ 12 * √ 3 / 2 - 3 = 1 - 3 - 3 = -5
3) cos t = - √(1 - sin²t) = - √(1 - (4/5)²) = -3/5
tg t = sin t / cos t = -4/3 ctg t = 1 / tg t = -3/4