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The solution set of inequality (tan^(-...

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.)

A

`(tan1, tan2)`

B

`(-cot1, cot2)`

C

`(-tan1, tan2)`

D

`(-tan1, oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(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`
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