if A,B, C,D be the angles of a quadrilateral then prove that sin A + Sin ( B, C,D)= 0​

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1. Question :

   If A,B,C and D are the angles of a quadrilateral, then sin (A+B)+sin(C+D) is equal to ?

   Answer :

   Since A,B,C,D are angles of quadrilateral

   A + B + C + D = 360 = 2 [tex]\pi[/tex]

   Therefore, sin(A+B)+sin(C+D)

   =sin(A+B)+sin(2π−(A+B))

   =sin(A+B)−sin(A+B)

   =0

   Hence answer is option C.

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