If sin(A + B) = 3 2 and tan(A - B) = 1 3 , then (2A + 3B) is equal to.

Answer: Option B

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)
$$\begin{array}{rl}& A+B=60^{\circ }\\ & \underline{A-B={30}^{\circ }}\\ & 2A=90^{\circ }\end{array}$$
A = 45°
B = 15°
(2A + 3B)
= (2 × 45° + 3 × 15°)
= 90° + 45°
= 135°