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All x satisfying the inequality (cot^(-...

All `x` satisfying the inequality `(cot^(-1) x)^(2) - 7 (cot^(-1) x) + 10 gt0` lie in the interval

A

`(cot 2 , oo)`

B

`(-oo, cot 5) uu (cot 2, oo)`

C

`(cot 5, cot 4)`

D

`(-oo , cot 5) uu (cot 4, cot 2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(cot ^(-1)x )^(2) -7 (cot ^(-1)x ) + 10 gt 0`
`(cot ^(-1) x -5) (cot ^(-1) x -2) gt 0`
`because cot ^(-1) x-5 lt 0 as cot ^(-1) x in (0,pi) implies cot ^(-1) x-2 lt 0`
`cot ^(-1) x lt 2 therefore x gt cot 2 " "(because cot ^(-1) x is darr)`
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