Complete solution set of `[cot^(-1)x]+2[tan^(-1)x]=0,` where `[]` denotes the greatest integer function, is equal to (a)`(0,cot1)` (b) `(0,tan1)` `(tan1,oo)` (d) `(cot1,tan1)`

Explanation

`[cot^-1x]+2[tan^-1x] = 0`

There can be two cases that satisfy the given equation.

Case -1 : When `[cot^-1x] = 0 and [tan^-1x] = 0`

`=> x in (cot1,oo) and x in (0,tan1)`

`=> x in (cot1,tan1).`

Case -2 : When `[cot^-1x] = 2 and [tan^-1x] = -1`

`=> x in (cot1,cot2] and x in [-tan1,0)`

`=> x in phi` as there is no intersection point of above two values of `x`.

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