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

`[cot^-1x]+[cos^-1x] = 0`

As, `cot^-1x and cos^-1 x ge 0`,

So, only solution available for this equation is,

`[cot^-1x] = [cos^-1x] = 0`

When `[cot^-1x] = 0, x in (cot1,oo)`

When `[cos^-1x] = 0, x in (cos1,1)`

Intersection of above two cases will be `x in (cot 1, 1)`.

So, option `c` is the correct option.