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    				| 1. | 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` | 
| Answer» Correct Answer - 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` | |