If sin (A + B) =1 and cos (A - B) = 1, 0° ≤ (A + B) ≤ 90° and A > B then find A and B.

Question

Philoid · Accepted Answer

Given: (i) sin (A + B) = 1

(ii) cos (A - B) = 1

Since, sin (A + B) = 1

⇒ sin (A + B) = sin 90° (∵ 0° ≤ (A + B) ≤ 90°, sin 90° = 1)

⇒ A + B = 90° .......................................... (1)

Also, cos (A - B) = 1

⇒ cos (A - B) = cos 0° (∵ 0° ≤ (A + B) ≤ 90°, cos 0° = 1)

⇒ A - B = 0° .......................................... (2)

From equation (2), we get A = B

Putting this value in equation (1), we get, 2A = 90° ⇒ A = 45°

∴ B = A = 45°

∴ A = B = 45°