If sin(A + B) = $$\frac{{\sqrt 3 }}{2}$$ and tan(A - B) = $$\frac{1}{{\sqrt 3 }}$$ , then (2A + 3B) is equal to.

sin(A + B) = $$\frac{{\sqrt 3 }}{2}$$
sin(A + B) = sin60°
A + B = 60° . . . . . . . .(i)
tan(A - B) = $$\frac{1}{{\sqrt 3 }}$$
tan(A - B) = tan30°
A - B = 30° . . . . . . . . (ii)
Equation (i) adding equation (ii)
$$\eqalign{ & A + B = {60^ \circ } \cr & \underline {A - B = {{30}^ \circ }} \cr & 2A\,\,\,\,\,\,\,\,\, = {90^ \circ } \cr} $$
A = 45°
B = 15°
(2A + 3B)
= (2 × 45° + 3 × 15°)
= 90° + 45°
= 135°