Question

A,B,C,D are the angles of a cyclic quadrilateral prove that sinA+sinB=sinC+sind

Answer 1

A+C=180°
A=180-C
sinA=sin (180-C)
sinA=sinC ..........(1)

B+D=180°
B=180-D
sin B= sin(180-D)
sinB= sinD ............(2)

From (1) and (2)
sinA+sinB=sinC+sinD