The number of distinct solutions of the equation 5 4 cos 2 ⁡   2 x + cos 4 ⁡ x + sin 4 ⁡ x + cos 6 ⁡ x + sin 6 ⁡ x = 2 in the interval [ 0 ,   2 π ] is

Step-by-step solution

5 4 cos 2 ⁡ 2 x + sin 2 ⁡ x + cos 2 ⁡ x 2 + sin 2 ⁡ x + cos 2 ⁡ x 3 - 5 sin 2 ⁡ x . cos 2 ⁡ x = 2 ⇒ 5 4 1 - sin 2 ⁡ 2 x - 5 4 sin 2 ⁡ 2 x + 2 = 2 ⇒ 1 - 2 sin 2 ⁡ 2 x = 0 ⇒ sin 2 ⁡ 2 x = 1 2   ⇒ 2 x = n π ± π 4 ⇒ x = n π 2 ± π 8 Number of solution = 8