Question

If ABCD is a cyclic quadrilateral then prove that sin A+sin B=sin C+sin D

Answer 1

Answer:

ANSWER

In a cyclic quadrilateral, sum of opposite angles is 180.

So, A+C=180⇒C=180−A⇒sinC=sin(180−A)=sinA

B+D=180⇒D=180−B⇒sinD=sin(180−B)=sinB

So,

sinA+sinB−sinC−sinD

=sinA+sinB−sinA−sinB

=0

Hence, A is correct.