If `[cot^(-1)x]+[cos^(-1)x]=0` , where `[]` denotes the greatest integer functions, then the complete set of values of `x` is (a)`(cos1,1)` (b) `cos1,cos1)` `(cot1,1)` (d) none of these

Explanation

We have `[cos^(-1)x] ge 0 AA x in [-1,1]`
and `[cot^(-1)x] ge 0 AA x in R`
Hence, `[cos^(-1)x]+[cot^(-1)x]=0`
only if `[cos^(-1)x]=[cot^(-1)x]=0`
`[cos^(-1)x]=0impliesx in (cos 1,1]`
`[cot^(-1)x]=0impliesx in (cot 1,oo)`
` :. x in (cot 1,1]`