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