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If $A$ and $B$ are acute angles such that $\sin (A - B) = 0$ and $2 \cos (A + B) – 1 = 0$, then find angles $A$ and $B$.
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Sol. $\sin (A - B) = 0 \Rightarrow A-B=0^\circ$
$\cos (A + B) = \frac{1}{2} \Rightarrow A + B = 60^\circ$
$\Rightarrow A = 30^\circ, B = 30^\circ$
$\cos (A + B) = \frac{1}{2} \Rightarrow A + B = 60^\circ$
$\Rightarrow A = 30^\circ, B = 30^\circ$