If $2 \sin(A + B) = \sqrt{3}$ and $\cos(A - B) = 1$, then find the measures of angles $A$ and $B$. $0 \leq A, B$, $(A + B) \leq 90°$.

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Step 1: $\sin(A + B) = \frac{\sqrt{3}}{2} \Rightarrow A + B = 60°$ ... (1)
Step 2: $\cos(A - B) = 1 \Rightarrow A - B = 0°$ ... (2)
Step 3: Solving (1) and (2), we get $A = B = 30°$

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