The sum of roots of the equation s i n 4 x - c o s 2 x s i n x + 2 s i n 2 x + s i n x = 0 for 0 ≤ x ≤ 3 π is equal to

Question

The sum of roots of the equation s i n 4 x - c o s 2 x s i n x + 2 s i n 2 x + s i n x = 0 for 0 ≤ x ≤ 3 π is equal to, 3 π 4, 2 π, 4 π, 6 π

MARKS App · Accepted Answer

s i n x s i n 3 x - c o s 2 x + 2 s i n x + 1 = 0 s i n x s i n 3 x + 2 s i n x + 1 - c o s 2 x = 0 s i n x s i n 3 x + s i n 2 x + 2 s i n x = 0 s i n 2 x s i n 2 x + s i n x + 2 = 0 ⇒ s i n x = 0 as s i n 2 x + s i n x + 2 ≠ 0 ⇒ x = n π , n ∈ I x ∈ 0,3 π , x = 0 , π , 2 π , 3 π ⇒ sum of roots = 6 π

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