Question

Помогите решить срочно 2sin^2x+15cos x+6=0

Answer 1

2sin²x + 15cosx + 6 =0
2(1-cos²x) + 15cosx + 6 = 0
2 - 2cos²x + 15cosx + 6 = 0
2cos²x - 15cosx - 8 = 0
cosx = t
2t² - 15t - 8 = 0
t₁ = (15+17)/4 = 8
t₂ = (15-17)/4 = -1/2

cosx = 8 ⇒ нет корней
cosx = -1/2

x = 2π/3 + 2πn
x = -2π/3 + 2πn

Ответ: -2π/3 + 2πn, 2π/3 + 2πn; n∈Z