Question

If `sin (A - B) = 1/2` and `cos (A + B) = 1/2`, 0° < (A + B) ≤ 90° and A > B then values of A and B are ______.

Options

• (60°, 30°)

• (60°, 15°)

• (45°, 15°)

• (60°, 25°)

Answer 1

If `sin (A - B) = 1/2` and `cos (A + B) = 1/2`, 0° < (A + B) ≤ 90° and A > B then values of A and B are (45°, 15°).

Explanation:

`sin (A - B) = 1/2 = sin 30^circ, cos (A + B) = 1/2 = cos 60^circ`.

∴ {A – B = 30° and A + B = 60°}

⇒ (A = 45°, B = 15°)