`-1lt cos(2x -(pi)/(3))lt(1)/(2)` has solution set

Options

A. `x in ((pi)/(3)+2n pi, (5pi)/(3)+2n pi), n in I`
B. `x in ((pi)/(3)+2n pi, (2pi)/(3)+2n pi)uu((2pi)/(3)+2n pi, (2n+1)pi), n in I`
C. `x in ((pi)/(3)+2n pi, pi+2n pi)uu(pi+2n pi, (5pi)/(3)+2n pi), n in I`
D. `x in ((pi)/(3)+n pi, (2pi)/(3)+n pi)uu((2pi)/(3)+n pi, (n+1)pi), n in I`

Answer

D

Explanation

`-1 lt cos (2x -(pi)/(3)) lt (1)/(2)` ………..
`(pi)/(3)lt 2x - (pi)/(3)lt pi uu pi 2x -(pi)/(3) lt (5pi)/(3)`
`(2pi)/(3)lt 2x lt(4pi)/(3)uu (4pi)/(3)lt 2x lt 2pi`
`(pi)/(3)lt x lt (2pi)/(3)uu (2pi)/(3)lt x lt pi`
general solution
`x epsilon ((pi)/(3)+n pi, (2pi)/(3)+n pi)uu((2pi)/(3)+n pi, (n+1)pi), n in I`