If $ \sin (A+B) =1$ and $\cos (A-B)= \large\frac{\sqrt 3}{2}, 0^{\circ} $$< (A+B) \leq 90^{\circ}, A > B $ then the value of A and B is ________

Question

$\begin{array}{1 1}(A) \;A=30^{\circ}; B= 60^{\circ} \\(B)\;A=15^{\circ}; B= 30^{\circ} \\(C)\;A=45^{\circ}; B= 60^{\circ} \\(D)\;A=60^{\circ}; B= 45^{\circ} \end{array}$