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Solve If [cos^(-1)x]+[cot^(-1)x]=0, wher...

Solve If `[cos^(-1)x]+[cot^(-1)x]=0,` where [.] denotes the greatest integer function, then the complete set of values of x is.

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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]`
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