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)`

Complete solution set of `[cot^(-1)x]+2[tan^(-1)x]=0,`where `[]`denote

1.	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)`
Answer» `[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`. So, only solution is possible in Case -1, that is, `x in (cot1,tan1)`. So, option `(d)` is the correct option.

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