The solution set of inequality
`(tan^(-1)x)(cot^(-1)x)-(tan^(-1)x)(1+(x)/(2))-2cot^(-1)x+2(1+(pi)/(2))gtlim_(yrarr-oo)[sec^(-1)y-(pi)/(2)]` is (where [ . ]denotes the G.I.F.)

Options

A. `(tan1, tan2)`
B. `(-cot1, cot2)`
C. `(-tan1, tan2)`
D. `(-tan1, oo)`

Answer

D

Explanation

`(tan^(-1)x-2)(cot^(-1)x-1-(pi)/(2))gt0`
`(tan^(-1)x+1)(tan^(-1)x-2)lt0`
`-1lt tan^(-1)xlt2,`
`implies-1 lt tan ^(-1) x lt (pi)/(2)`
`implies -tan1 lt x lt oo`