UPSC NDA Math Model Paper 6

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