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

If A,B,C,D are the angles of a cyclic quadrilateral then cos A + cos B+ cos C + cos D=

I: If A,B,C,D are angles of a cyclic quadrilateral then cos A + cos B + cos C + cos D=0 II : If A,B,C,D are the angles of a quadrilateral then cos""(A+B)/(2) + cos""(C+D)/(2) =0

If A, B, C are angles of a triangle , prove that cos 2A - cos 2B + cos 2C =1 -4 sin A cos B sin C

If ABCD is a cyclic quadrilateral then show that i) cos A + cos B + cos C + cos D = 0 ii) sin A + sin B = sin C + sin D

If A, B, C are angles of a triangle , prove that cos 2A+cos 2B -cos 2C=1-4 sin A sin B cos C

Assertion (A): If A, B, C are the angles of a triangle such that cos A + cos B + Cos C = 0 = sin A + sin B + sin C then cos 3A + cos 3B + cos 3C = -3 Reason (R) : If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + singamma then cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos (gamma+alpha+beta)

If A , B , C are angles in a triangle , then prove that sin A + sin B + sin C =4 cos. (A)/(2) cos . (B)/(2) cos .(C)/(2)