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If tan(A-B)=1a n dsec(A+B)=2/(sqrt(3)) ,...

If `tan(A-B)=1a n dsec(A+B)=2/(sqrt(3))` , then the smallest positive values of A and B, respectively, are `(25pi)/(24),(19pi)/(24)` (b) `(19pi)/(24),(25pi)/(24)` `(31pi)/(24),(31pi)/(24)` (d) `(13pi)/(24),(31pi)/(24)`

A

`(25 pi)/(24), (19 pi)/24`

B

`(19 pi)/24, (25 pi)/24`

C

`(31 pi)/24, (13 pi)/24`

D

`(13pi)/24, (31 pi)/24`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan (A-B)=1`
`rArr A-B=n_(1) pi+pi/4 or A-B=pi/4, (3pi)/4, -(3pi)/4`, ...
`sec(A+B) =2/sqrt(3)`
`rArr A+B=2n_(2)pi pm pi/6 or A+B=pi/6, (11 pi)/6`, ...
For the least positive values of A and B, we have
`A+B=(11pi)/6, A-B=pi/4`
`rArr B=(19 pi)/24, A=(25 pi)/24`
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