Question

In a cyclic quadrilateral ABCD, prove that sin A = sin C

[ class 11] ​

Answer 1

Step-by-step explanation:

In A Cyclic Quadrilateral,

Sum of All Opposite Angles in Cyclic quad = 180⁰

so,

Angle A + Angle C = 180⁰

Angle C = 180⁰ - Angle A.

RHS = SIN C = sin ( 180⁰ - Angle A) = Sin A = LHS

RHS = LHS .

Hence Proved.

Answer 2

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.

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