Question

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

Answer 1

Answer:

Step-by-step explanation:

A+C=180°,B+D=180°

A=180°-C,B=180°-D

sin A+sin B-sin C-sin D=sin(180°-C)+sin(180°-B)-sin C-sin D=sin C+sin D -sin C-sin D=0

sin A+sin B=sin C+sin D

Answer 2

Concept

• In Euclidean geometry, an inscribed quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices are all on a circle.
• This circle is called the circumcircle or circumscribed circle, and the vertices are said to be circles

Given

The cyclic quadrilateral ABCD

Find

We ha ve to prove sin A + sin B = sin C + sin D

Solution

• The steps are as follow:

∠A + ∠C = 180

∠A = 180-∠C

∠B + ∠D = 180

∠B = 180-∠D

• So

sinA+sinB-sinC-sinD

= sin(180-C)+sin(180-D)-sinC-sinD

= sinC+sinD-sinC-sinD

= 0

Hence proved sin A + sin B = sin C + sin D for a cyclic quadrilateral ABCD

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