Find A and B,if sin(A-B)=1/2 and cos(A+B)=1/2

We know that Sin 30=1/2 and that cos 60= 1/2
Thus A+B=60 and A-B=30 =>A=30+B
Thus, 30+B+B=60
2B=30
B=15
A=30+B=30+15
A=45