Let S = θ ∈ - 2 π , 2 π : 2 cos 2 θ + 3 sin θ = 0 . Then the sum of the elements of S is:

Step-by-step solution

The given equation 2 cos 2 θ + 3 sin θ = 0 can be written as 2 1 - sin 2 θ + 3 sin θ = 0 ⇒ 2 s i n 2 θ - 3 s i n θ - 2 = 0 ⇒ 2 sin θ + 1 sin θ - 2 = 0 ⇒ sin θ = 2 ,   - 1 2 ,   sin θ ≠ 2 ⇒ sin θ = - 1 2 Hence, solutions in - 2 π ,   2 π are - π + π 6 ,   - π 6 ,   π + π 6 ,   2 π - π 6 Sum of the elements is = 2 π .