Question

If A, B, C, D are angles of a cyclic quadrilateral, prove that: cos A + cos B + cos C + cos D = 0.

Answer 1

In a cyclic quadrilateral sum of opposite angles are 180°.

Since A, B, C, D are angles of cyclic quadrilateral

A + C = 180° and B + D = 180°

LHS = 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

= 0

= RHS