If \(tan\ (A-B)=\frac{1}{\sqrt{3}}\), \(cos\ (A+B) =\frac{1}{2}\), \(0^{\circ}<A+B\le 90^{\circ}\), \(A>B\), work out \(A\) and \(B\).
 
Answer:
 
\(A =\) i°
 
\(B =\) i°