If sin (A - B) = 1/2 and tan (A + B) = √3, where 0° ≤ A + B B, fin...

Question

If sin (A - B) = 1/2 and tan (A + B) = √3, where 0° ≤ A + B  B, find the values of A and B.

Accepted Answer

$\sin(A-B)=\frac12 \Rightarrow A-B=30°$
$	an(A+B)=\sqrt3 \Rightarrow A+B=60°$
Adding: $2A=90° \Rightarrow A=45°$. Then $B=60°-45°=15°$.
**A = 45°, B = 15°**

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