if cos(a-b)=1/2 and sin(a+b)=1/2 find smallest positive values of a and b and also their most general values

cos(a-b)=1/2, a-b=2nPi+Pi/3

SINCE WE NEED TO FIND THE SMALLEST POSSIBLE VALUE FOR a & b both a & b should lie in first quadrant and SIN(a+b)=1/2 ===>>> SIN(a+b)=SIN (pi/6)=====>> a+b=pi/6.........(1) COS(a-b)=1/2 ===>>>COS(a+b)=COS(pi/3)=====>> a-b=pi3..........(2) solve for a and b===>> a=pi/4 b=pi/6