The set of all values of x, measured in radians, satisfying the two inequalities
`2 cos^(2)x lt 2-3 cos x` and `x^(2) lt 4x+12`, is

Options

A. `(-2,-pi//3)cup(pi//3,5pi//3)`
B. `(pi//3,pi//2)cup(3pi//2,2//pi)`
C. (-2,6)
D. `(-2,1//2)`

Answer

A

Explanation

We have,
`2cos^(2) x lt 2-3 cos x` and `x^(2) lt 4x+12`
Now,
`2cos^(2) xlt 2-3 cos x`
`implies 2 cos^(2)x+3 cos x -2 lt 0`
`implies (2 cos x-1)(cos x+2) lt 0`
`implies