If 4 sin 2 x sin 4 x + sin 2 x = 3 , then x =

Question

If 4 sin 2 x sin 4 x + sin 2 x = 3 , then x =, 2 n π 3 ± π 9 , n ∈ Z, m π 3 ± π 9 , n ∈ Z, n π 3 + ( - 1 ) n π 9 , n ∈ Z, n π 3 + ( - 1 ) n 2 π 9 , n ∈ Z

MARKS App · Accepted Answer

Simplify the given expression 4 sin 2 x sin 4 x + sin 2 x = 3 ⇒ 2 ( cos 2 x - cos 6 x ) + 2 ( 1 - cos 2 x ) = 3 ⇒ 2 cos 2 x - 2 cos 6 x + 2 - 2 cos 2 x = 3 ⇒ - 2 cos 6 x + 2 = 3 ⇒ cos 6 x = - 1 2 Therefore, 6 x = 2 π n ± 2 π 3 ⇒ x = 2 n π 6 ± 2 6 × π 3 ⇒ x = n π 3 ± π 9

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