Find A and B,if sin(A-B)=1/2 and cos (A+B)=0

We know that Sin 30 = 1/2 
Therefore, A-B=30 =>A=30+B......(1)
And that Cos 90=0
Therefore A+B=90......(2)
Substitute the values now:
30+2B=90
2B=60
B=30
Therefore since A+B=90, A=60