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

Solve `[cot^(-1) x] + [cos^(-1) x] =0`, where `[.]` denotes the greatest integer function

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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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