2(2Cos²x -1) +4√3Cosx -7 = 0
4Cos²x -2 +4√3Cosx - 7 = 0
4Cos²x +4√3Cosx -9 = 0
Cosx = t
4t² +4√3 t -9 = 0
t = (-2√3+-√48)/4 = (-2√3 +-4√3)/4
t₁ = -6√3/4 t₂= 2√3/4
Cost = -3√3/2 Cosx = √3/2
∅ x = +-arcCos√3/2 +2πk , k ∈ Z
x = +-π/6 + 2πk , k ∈ Z
в указанный промежуток попадают числа:5π/2 + π/6 = 8π/3
7π/2 - π/6 = 10π/3
7π/2 + π/6 = 11π/3