If tanA−B=1,secA+B=23, then least positive values of A, B are
25π24,19π24
19π24,25π24
31π24,13π24
13π24,31π24
We have tanA−B=1⇒tanA−B=tanπ4 ⇒A−B=nπ+π4
⇒A-B=π4,5π4,9π4,....
Also secA+B=23⇒cosA+B=32=cosπ6 ⇒A+B=2nπ±π6=π6,11π6,13π6....
Since A and B are to be the least positive values, we must have A-B=π4 and A+B=11π6 ⇒2A=50π24⇒A=25π24 Also 2B=38π24⇒B=19π24