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:

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Correct answer: D. 8

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 ⁡ x - cos 4 ⁡ x + 18 cos 2 ⁡ x - sin 2 ⁡ x = 1 ± 2 2 cos 4 ⁡ x + 18 sin 2 ⁡ x ⇒ 2 sin 2 ⁡ x - cos 2 ⁡ x + 18 cos 2 ⁡ x - sin 2 ⁡ x = 1 ± 2 2 cos 4 ⁡ x + 18 sin 2 ⁡ x ⇒ 16 cos 2 ⁡ x - sin 2 ⁡

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:

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