If $sin (A - B) =\frac{1}{2}$ and $cos(A +B)=\frac{1}{2}$, where A > B > 0° and A + B is an acute angle, then the value of A is:

45° 30° 15° 60°

45°

$sin (A - B) =\frac{1}{2}$ We know, sin30º = \(\frac{1 }{2}\) So , ( A - B ) = 30º        ------(1) And, cos ( A + B ) = \(\frac{1 }{2}\) cos 60º = \(\frac{1 }{2}\) ( A + B ) = 60º    ------(2) On Adding 1 and 2 2A = 90º A = 45º