Question

Упростите выражения: а)cos 2t - cos²t / 1 - cos ² t

б) sin 2t - 2sin t / cos t - 1​

Answer 1

Ответ:

Объяснение:

а) cos 2t - cos²t / 1 - cos ² t

cos 2t - cos²t = cos 2t - (1 - sin²t) = sin²t - cos 2t

(sin²t - cos 2t) / (1 - cos²t)

(sin²t - cos 2t) / sin²t

б) sin 2t - 2sin t / cos t - 1

sin 2t - 2sin t / cos t - 1 = 2sin t cos t / (cos t - 1) - 2sin t / (cos t - 1)

2sin t cos t - 2sin t / (cos t - 1) = 2sin t (cos t² - 1) / (cos t - 1)

2sin t (cos t² - 1) = -2sin t sin t² = -2sin³ t

sin 2t - 2sin t / cos t - 1 = -2sin³ t / (cos t - 1)