Find the solution set for , ` 4 sin^(2)x -8 sin x +3 le 0` where ` x in [0,2pi]`

Options

A. `[0, pi//6]`
B. `[0, 5pi//6]`
C. `[5pi//6, 2pi]`
D. `[pi//6, 5pi//6]`

Answer

D

Explanation

We have,
`4"sin"^(2) x - 8 "sin" x + 3 le 0`
`rArr (2"sin" x-1) (2"sin" x-3) le 0`
`rArr 2 "sin" x-1 ge 0 " " [because 2 "sin" x-3 le 0 " for all "x]`
`rArr "sin" x ge (1)/(2)`
`rArr x in [pi//6, 5pi//6] " " ["Draw graph of y = sin x and find the values"]`