If `cosec^(-1)(cosecx)` and `cosec(cosec^(-1)x)` are equal functions, then the maximum range of value of `x` is (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]`

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)]`