Given: (i) tan (A - B) = 1/√3

(ii) tan (A + B) = √3

Since, tan (A - B) = 1/√3

⇒ tan (A - B) = tan 30° (∵ 0° < (A + B) < 90°, tan 30° = 1/√3)

⇒ A - B = 30° .......................................... (1)

Also, tan (A + B) = √3

⇒ tan (A + B) = tan 60° (∵ 0° < (A + B) < 90°, tan 60° = √3)

⇒ 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°