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If 2 sin^(2)(x-(pi)/(3))-5sin(x-(pi)/(3)...

If `2 sin^(2)(x-(pi)/(3))-5sin(x-(pi)/(3))+2lt0`, then belongs tp

A

`(((12n-5)pi)/(6),((4n+1)pi)/(2)),n in Z`

B

`(((6n-7)pi)/(6),((2n+1)pi)/(2)),n in Z`

C

`(((4n+1)pi)/(6),n pi),n in Z`

D

`((4n+1)(pi)/(2),(12n+7)(pi)/(6)),n in Z`

Text Solution

Verified by Experts

The correct Answer is:
D
`2sin^(2)(x-(pi)/(3))-5 sin(x-(pi)/(3))+2 lt 0`
`rArr (2 sin(x-(pi)/(3))-1)(sin(x-(pi)/(3))-2)lt0`
`rArr (1)/(2)lt sin (x-(pi)/(3))lt2`
`rArr (1)/(2)lt sin (x-(pi)/(3))le 1`
`therefore x-(pi)/(3)in (2n pi + (pi)/(6), 2n pi+(5pi)/(6))`
`x in (2n pi+(pi)/(2), 2n pi+(7pi)/(6)), n in I`
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