Given: ABCD is a cyclic quadrilateral Therefore, A + C = 180° and B + D = 180° ⇒ C = 180° - A and D = 180° - B Now, sin A + sin B - sin C - sin D = sin A + sin B - sin (180° - A) - sin (180° - B) = sin A + sin B - sin A - sin B (∵ sin (180° - θ) = sin θ) = 0