Question

If $A,B,C,D$ are the angles of a cyclic quadrilateral, then $\cos A+\cos B+\cos C+\cos D$ is equal to

• A. $-1$
• B. zero
• C. $-2$
• D. $1$

Answer 1

The correct option is B zero

$\because ABCD$ is cyclic quadrilateral
$\therefore A+C=\pi$ and $B+D=\pi$
$\Rightarrow A=\pi -C$ and $B=\pi -D$
Now, $\cos A+\cos B+\cos C+\cos D$
$=\cos (\pi -C)+\cos (\pi -D)+\cos C+\cos D$
$=-\cos C-\cos D+\cos C+\cos D$
$=0$