Question

If $\square ABCD$ is a cyclic quadrilateral, then find which of the following statement is not correct?

• A. $\sin (A+C)=0$
• B. $\sin (A+B)=0$
• C. $\cos (B+D)=-1$
• D. $\sin (A+B+C+D)=0$

Answer 1

Answer: (B)

$\sin (A+B)=0$

In a cyclic quadrilateral ABCD, sum of opposite angles is $\pi$
Therefore, $A+C=B+D=\pi$
and $A+B+C+D={360}^0$

Hence, $\sin (A+C)=\sin (B+D)=0$
$\cos (A+C)=\cos (B+D)=\cos \pi =-1$
$\sin (A+B+C+D)=\sin \left({360}^0\right)=0$
Therefore, B is false.