The number of x ∈ 0 , 2 π for which 2 sin 4 x + 18 cos 2 x - 2 cos 4 x + 18 sin 2 x = 1 is:

Step-by-step solution

Given 2 sin 4 ⁡ x + 18 cos 2 ⁡ x -   2 cos 4 ⁡ x + 18 sin 2 ⁡ x = 1 ⇒ 2 sin 4 ⁡ x + 18 cos 2 ⁡ x -   2 cos 4 ⁡ x + 18 sin 2 ⁡ x =   ± 1 ⇒ 2 sin 4 ⁡ x + 18 cos 2 ⁡ x =   ± 1 +   2 cos 4 ⁡ x + 18 sin 2 ⁡ x By squaring both the sides, we get 2 sin 4 ⁡ x + 18 cos 2 ⁡ x = 1 + 2 cos 4 ⁡ x + 18 sin 2 ⁡ x ± 2 2 cos 4 ⁡ x + 18 sin 2 ⁡ x ⇒  2 sin 4 ⁡