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If cos(A + B) = 1/2 and sin(A − B) = 1/2, where 0° < A + B ≤ 90° and A > B, find A.

Competition practiceTrigonometry

A45°
B15°
C30°
D60°

Step-by-Step Solution

cos (A + B) = \frac{1}{2}

gives

A + B = 6 0^{\circ}

;

sin (A - B) = \frac{1}{2}

gives

A - B = 3 0^{\circ}

. Adding,

2 A = 9 0^{\circ}

, so

A = 4 5^{\circ}

(and

B = 1 5^{\circ}

).

Answer: A) 45°

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