3. trignometrical ratios,functions and identities — ગણિત ધોરણ 11 સાયન્સ — Question

since $ABCD$ is a cyclic quadrilateral.

$ \Rightarrow A = 180^\circ - C$

$ \Rightarrow \cos A = \cos (180^\circ - C) = - \cos C$

$ \Rightarrow \cos A + \cos C = 0$.....$(i)$

Now $B + D = 180^\circ ,$ then $\cos B + \cos D = 0$.....$(ii) $

Subtracting $(ii)$ from $(i),$ we get

$\cos A - \cos B + \cos C - \cos D = 0$.