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If sin (A – B) = (1 / 2) and cos (A + B) = (1 / 2) where A > B > 0 and A + B is an acute angle, then the value B is
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π 6 -
π 12 -
π 4 -
π 2
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Correct Option: B
| sin (A – B) = | = sin 30° | 2 |
⇒ A - B = 30°
| Again, cos (A + B) = | = cos 30° | 2 |
⇒ A + B = 60°
∴ A + B + A – B = 30° + 60° = 90°
⇒ 2 A = 90°
⇒ A = 45°
∴ A - B = 30°
⇒ B = A - 30° = 45° - 30° = 15°
| = | = | radian | 180 | 12 |
