Find
(a) tan (x+y),
(b) tan (x-y),
(c) the quadrant containing (x+y), and
(d) the quadrant containing (x-y).
Given:
tan x = 2/3, 0 < x < π/2 ;
tan y = 5/6, 0 < y < π/2.
just plug the numbers into the sum/difference formulas. Surely you can do that...
Since both x and y are less than π/4 (why?), x+y is in QI.
Since y > x, x-y is in QIV.