15) 2cos(4x-π/6)=√3

15) 2cos(4x - π/6) = √3

cos(4x - π/6) = √3/2

4x - π/6 = ±arccos(√3/2) + 2πn, n ∈ Z

4x - π/6 = ±π/6 + 2πn, n ∈ Z

4x = π/6 ± π/6 + 2πn, n ∈ Z

x = π/24 ± π/24 + πn/2, n ∈ Z

x₁ = π/12 + πn/2, n ∈ Z

x₂ = πn/2, n ∈ Z

Ответ: x₁ = π/12 + πn/2, n ∈ Z; x₂ = πn/2, n ∈ Z