4cos^2(x-π/6) - 3 = 0
cos^2(x-π/6) = 3/4
cos(x-π/6) = ±√(3/4)
cos(x-π/6) = ±√3/2
x-π/6 = ±π/6
x = π/6 ± π/6, 7π/6 ± π/6
Ответ: x = π/3, 2π/3, 5π/3, 11π/3.
4cos^2(x-π/6) - 3 = 0
cos^2(x-π/6) = 3/4
cos(x-π/6) = ±√(3/4)
cos(x-π/6) = ±√3/2
x-π/6 = ±π/6
x = π/6 ± π/6, 7π/6 ± π/6
Ответ: x = π/3, 2π/3, 5π/3, 11π/3.