решите уравнение 8sin²x-2cosx-5=0. решите уравнение 8sin²x-2cosx-5=0

8sin(x) - 2cos(x) - 5 = 0

8(1 - cos(x)) - 2cos(x) - 5 = 0

8 - 8cos(x) - 2cos(x) -5 = 0

8cos(x) + 2cos(x) - 3 = 0

cos(x) = 1/2 --> x = ±π/3 + 2πk

cos(x) = -3/4 --> x = ±arccos(-3/4) + 2πk

Ответ: ±π/3 + 2πk, ±arccos(-3/4) + 2πk, k - целое.