Question

If $A,B,C,D$ are the angles of a cyclic quadrilateral, then the value of $\sec A+\sec B+\sec C+\sec D$ is

Answer 1

As $ABCD$ is cyclic quadrilateral
$\therefore A+C=\pi$ and $B+D=\pi$
$\Rightarrow A=\pi -C$ and $B=\pi -D$

Now,
$\sec A+\sec B+\sec C+\sec D=\sec (\pi -C)+\sec (\pi -D)+\sec C+\sec D=-\sec C-\sec D+\sec C+\sec D=0$