If `cosec^(-1) (cosec x) and cosec (cosec^(-1) x)` are equal function then the maximum range of value of x is

Options

A. `[-(pi)/(2), -1] uu [1, (pi)/(2)]`
B. `[-(pi)/(2), 0)uu[0, (pi)/(2)]`
C. `(-oo, -1] uu [1, oo)`
D. `[-1, 0) uu [0, 1)`

Answer

A

Explanation

`cosec (cosec^(-1) x) = x AA x in R -(-1, 1)`
Also range of `cosec^(-1) (cosec x) in [-(pi)/(2), 0) uu (0, (pi)/(2]`
So combing these two, we get
`x in [-(pi)/(2), -1] uu [1, (pi)/(2)]`