If sin (A - B) = 1/2 and cos (A +B) = 1/2 ,0° < (A + B) < 90° and A > B then find A and B.
Given: (i) sin (A - B) = 1/2
(ii) cos (A + B) = 1/2
Since, sin (A - B) = 1
⇒ sin (A - B) = sin 30° (∵ 0° < (A + B) < 90°, sin 30° = 1/2)
⇒ A - B = 30° .......................................... (1)
Also, cos (A + B) = 1/2
⇒ cos (A + B) = cos 60° (∵ 0° < (A + B) < 90°, cos 60° = 1/2)
⇒ A + B = 60° .......................................... (2)
On adding equation (1) and (2), we get,
2A = 90° ⇒ A = 45°
Putting this value in equation (2), we get,
B = 60° - A = 60° - 45° ⇒ B = 15°
∴ ∠A = 45°, ∠B = 15°