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If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| l...

If `|cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3)`, then

A

`x in [-(1)/(3), (1)/(sqrt3)]`

B

`x in (-(1)/(sqrt3), (1)/(sqrt3))`

C

`x in (0, (1)/(sqrt3))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`|cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3)`
`rArr -(pi)/(3) lt cos^(-1) ((1 -x^(2))/(1 + x^(2))) lt (pi)/(3)`
`rArr 0 le cos^(-1).(1 -x^(2))/(1 + x^(2)) lt (pi)/(3)`
`rArr (1)/(2) lt (1 - x^(2))/(1 + x^(2)) le 1`
`rArr 1 + x^(2) lt 2 (1 -x^(2)) le 2 (1 + x^(2))`
`rArr 0 le x^(2) lt (1)/(3)`
`rArr -(1)/(sqrt3) lt x lt (1)/(sqrt3)`
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