The set of value of ` theta ` satisfying the inequation ` 2 sin^(2) theta - 5 sin theta +2 gt 0, "where " 0 lt theta lt 2 pi `, is

Options

A. `(0, (pi)/(6)) cup ((5pi)/(6), 2pi)`
B. `[0, (pi)/(6)] cup [(5pi)/(6), 2 pi]`
C. `[0, (pi)/3)] cup [(2pi)/(3), 2 pi]`
D. none of these

Answer

B

Explanation

We have,
`2"sin"^(2) theta - 5"sin" theta + 2 gt 0`
`rArr (2"sin" theta -1) ("sin" theta - 2) gt 0`
`rArr 2 "sin" theta - 1 lt 0 " " [because "sin" theta -2 lt 0]`
`rArr "sin" theta lt (1)/(2)`
`rArr theta in (0, (pi)/(6)) cup ((5pi)/(6), 2 pi)`