The least positive solution of cot⁡π33sin⁡2x=3 lies in

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0,π6

π9,π6

π12,π9

π3,π2

answer is A.

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Detailed Solution

cot⁡π33sin⁡2x=3⇒ π33sin⁡2x=nπ+π6,n∈Z⇒ sin⁡2x=33n+32for solution n= 0⇒ sin⁡2x=32⇒ 2x=π3⇒x=π6

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