If sin(A + B)Â = 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) = $$\frac{\sqrt{3}}{2}$$
$$\Rightarrow$$Â sin(A + B) = sin 60
$$\Rightarrow$$Â A + B =Â 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 = 90Â $$\Rightarrow$$ A = 45
Substituting A = 45 in equation (1)
45 + B = 60Â $$\Rightarrow$$ B = 15
$$\therefore\ $$ A = 45 and B = 15
Hence, the correct answer is Option B
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