Question

If A, B, C, D are angles of a cyclic quadrilateral, then
$\cos A+\cos B+\cos C+\cos D=$

Answer 1

We know that the opposite angles of a cyclic quadrilateral are supplementary,

i.e., $A+C=\pi$ and $B+D=\pi$.

Therefore,
$A=\pi -C$ and $B=\pi -D$

$\Rightarrow$ $\cos A=\cos (\pi -C)=-\cos C$

and $\cos B=\cos (\pi -D)=-\cos D$

$\therefore$ $\cos A+\cos B+\cos C+\cos D=-\cos C-\cos D+\cos C+\cos D=0$
Ans: 0