posted by diviya .
if sinA+sinB=x and cosA-cosB=y then find tan[(A-B)/2]
I don't know how many trig ratios of half-angles you have developed or know but here is a page where many of them are done.
about 2/3 of the way down you should find
tan [(A+B)/2) = (sinA +sinB)/(cosA + cosB)