if sinA+sinB=x and cosA-cosB=y then find tan[(A-B)/2]

Answer 1

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.
http://www.intmath.com/analytic-trigonometry/4-half-angle-formulas.php

about 2/3 of the way down you should find
tan [(A+B)/2) = (sinA +sinB)/(cosA + cosB)
= x/y

Answer 2

-y/x

Answer 3

I think you should use the Power Reducing or Half Angle Formula in Trigonometry.

Check out this link for the list of formulas - <a href="www.teachoo.com/9723/1412/Trigonometry-Formulas/category/2-sin-x-sin-y-formula/"> Trigonometry Formulas </a>