Question

ABCD is a cyclic quadilateral then the value of $\cos A+\cos B+\cos C+\cos D$

• A. 0
• B. 1
• C. $2(\cos A+\cos B)$
• D. None of these

Answer 1

Answer: (A)

0

In cyclic quadilateral,

$\angle A+\angle C={180}^o$

$\angle B+\angle D={180}^o$
Now, $\cos A+\cos B+\cos C+\cos D$

$=\cos (180-C)+\cos (180-D)+\cos C+\cos D$

$=-\cos C-\cos D+\cos C+\cos D$

$=0$

$\Rightarrow \cos A+\cos B+\cos C+\cos D=0$