If $\sin(A - B) = \frac{1}{2}$, $\cos(A + B) = \frac{1}{2}$; $0 B$; find $\angle A$ and $\angle B$.

Question

If $\sin(A - B) = \frac{1}{2}$, $\cos(A + B) = \frac{1}{2}$; $0 < A + B \leq 90°$, $A > B$; find $\angle A$ and $\angle B$.

Accepted Answer

Step 1: $\sin(A - B) = \sin 30° \Rightarrow A - B = 30°$ ... (i)
Step 2: $\cos(A + B) = \cos 60° \Rightarrow A + B = 60°$ ... (ii)
Step 3: Solving (i) and (ii): $A = 45°$, $B = 15°$

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