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

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

A

`(cos 1,1]`

B

`(cos 1, cot1)`

C

`(cot 1, 1]`

D

none of these

Text Solution

Verified by Experts

We have
`cot^(-1) x in [0,pi] and cos^(-1) x in [0,pi]`
`therefore [cost(-1)x]gt0 and [cos^(-1)x]ge0`
Now `[cos^(-1)x]=0 =[cos^(-1)xlt1`
`rarr cot 1 ltx lt infty and cos 1 lt x le 1`
`rarr fx in (cot1,infty) and x in (cos 1,1]rarr x in (cot1,1]`
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