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If all values of `x in (a, b)` satisfy the inequality `tan x tan 3x lt -1, x in (0, (pi)/(2))`, then the maximum value (b -a) is :

A

`(pi)/(12)`

B

`(pi)/(3)`

C

`(pi)/(6)`

D

`(pi)/(4)`

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The correct Answer is:
A
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