The number of elements in the set S = θ ∈ - 4 π , 4 π : 3 cos 2 2 θ + 6 cos 2 θ - 10 cos 2 θ + 5 = 0 is ______.

Step-by-step solution

3 cos 2 2 θ + 6 cos 2 θ - 10 cos 2 θ + 5 = 0 3 cos 2 2 θ + 6 cos 2 θ - 5 1 + cos 2 θ + 5 = 0 cos 2 θ 3 cos 2 θ + 1 = 0 cos 2 θ = 0 or cos 2 θ = - 1 3 Given θ ∈ - 4 π , 4 π ⇒ 2 θ ∈ - 8 π , 8 π So for 2 θ = 2 n + 1 π 2   θ = ± π 4 , ± 3 π 4 , … … … ± 15 π 4 gives 16 solution Similarly cos 2 θ = - 1 3 gives 16 solution hence, total elements in set S