UPSC NDA Math Model Paper 8

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