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All x satisfying the inequnality (cot^...

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

A

`(-oo, cot5) nn(cot2,oo)`

B

`(cot5,cot4)`

C

`(cot2,oo)`

D

`(-oo,cot5),(cot4,cot2)`

Text Solution

Verified by Experts

The correct Answer is:
c
Given, `(cot^(-1)x)^(2)-7(cot^(-1)x)+10gt0`
`implies(cot^(-1)x-2)(cot^(-1)x-5)gt0" "("by factorisation")`
`impliescot ^(-1)xlt2" or "cot^(-1)xgt5`
By wavy curve method
`:." "cot^(-1)x in(-oo,2)uu(k,oo)`
`cot^(-1)x in(0,2)" "[because"Range of "cot^(-1)" is "(0,pi)]`
`:." "x in(cot2,oo)`
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