2sin x*cos x - sqrt(3)*sin x = 0
sin x*(2cos x - sqrt(3)) = 0
Если произведение равно 0, то один из множителей равен 0.
1) sin x = 0
x = π*k, k ∈ Z
2) 2cos x - sqrt(3) = 0
cos x = sqrt(3)/2
x = ± π/6 + 2π*n, n ∈ Z
б) Корни, принадлежащие [3π/2; 5π/2] = [9π/6; 15π/6]
x1 = 2π
x2 = -π/6 + 2π = -π/6 + 12π/6 = 11π/6
x3 = π/6 + 2π = π/6 + 12π/6 = 13π/6
Ответ: 11π/6; 2π; 13π/6