The function `f(x)=cos^(-1)((2[|sinx|+|cosx|])/(sin^2x+2sinx+11/4))` is defined if x belongs to (where [.] represents the greatest integer function)

Options

A. `[0,(7pi)/(6)]`
B. `[0,(pi)/(6)]`
C. `[(11pi)/(6)]`
D. `[pi,2pi]`

Answer

A, B, C

Explanation

`1le|sinx|+|cosx|lesqrt2`
`therefore" "2[|sinx|+|cosx|]=2`
`thereforef(x)` is defined if
`sin^(2)x+2 sin x+(11)/(4)ge2`
`"or "(sinx+1)^(2)ge(1)/(4)`
`"or "sinx+1ge(1)/(2) or sin x+1le-(1)/(2)`
`"or "sinx ge-(1)/(2) or sin le-(3)/(2)` (which is not true)