First slide

Trigonometric Identities

Question

In a cyclic quadrilateral ABCD, the value of $\cos A + \cos B + \cos C + \cos D$ is

Moderate

A

1
B

0
C

-1
D

none of these

Solution

In cyclic quadrilateral ABCD, we have
$\begin{array}{l} A + C = π and B + D = π \\ ∴ \cos A = - \cos C and \cos B = - \cos D \\ \Rightarrow \cos A + \cos B + \cos C + \cos D = 0 \end{array}$

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