Question

A,B,C,D are angles of a cyclic quadrilateral then sinA+sinB- sinC-sinD​

Answer 1

Answer:

0

Step-by-step explanation:

In a cyclic quadrilateral, opposite angles sum is 180

A + C = 180 --------------(i)

B + D = 180 --------------(ii)

From equation first

A=180-C

sinA=sin (180-C)

sinA=sinC

sinA-sinC=0

similarly From equation second

sinB-sinD=0

L.H.S= sinA+sinB-sinC-sinD

= (sinA-sinC)+sinB-sinD

=0

Answer 2

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