If sin(A + B) = cos(A - B) = $$\frac{\sqrt{3}}{2}$$ and A and B are acute angles. The measures of angles A and B (in degrees)will be:

Given, sin(A + B) = $$\frac{\sqrt{3}}{2}$$

$$\Rightarrow$$  sin(A + B) = sin 60

$$\Rightarrow$$  A + B = 60 .......(1)

cos(A - B) = $$\frac{\sqrt{3}}{2}$$

$$\Rightarrow$$ cos(A - B) = cos 30

$$\Rightarrow$$ A - B = 30 ........(2)

Adding equation(1) and equation(2),

2A = 90 $$\Rightarrow$$ A = 45

Substituting A = 45 in equation (1)

45 + B = 60 $$\Rightarrow$$ B = 15

$$\therefore\ $$ A = 45 and B = 15

Hence, the correct answer is Option B