Question

If $ABCD$ is a cyclic quadrilateral, then find which of the following statements 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

The correct option is B $\sin (A+B)=0$

In cyclic quadrilateral $A+C={180}^{\circ }$ and $B+D={180}^0$
$\therefore \sin (A+C)=\sin {180}^{\circ }=0$ option $A$ is true.
$\cos (B+D)=\cos {180}^{\circ }=-1$ option $C$ is true.
$\sin (A+B+C+D)=\sin {360}^{\circ }=0$ option $D$ is true.
Clearly option $B$ is incorrect.