Find all solutions of the equation 2 sin x + √ 3 = 0 . The answer is A + B k π and C + D k π where k is any integer, 0 < A < C < 2 π ,

Answer 1

2 sin x + √ 3 = 0

simplify this to get sin x = - √ 3 / 2

Which gives us x = π + π/3, 2π - π/3, 3π + π/3, 4π - π/3,......

For the answers to fit into A + B k π and C + D k π, where 0 < A < C < 2 π

The solution is x = π + π/3, A = π, B = 1/3, k = 1

and x = 3π/2 + π/6, where C =3π/2, D = 1/6, k = 1