Question

If A, B, C, D, are the angles of cyclic quadrilateral, then cosA + cosB + cosC + cosD =

• A. 2(cosA + cosC)
• B. 2 (cosB + cosD)
• C. 2 (cosA + cosD)
• D. 0

Answer 1

The correct option is D

0

Since A, B, C, D is the angles of cyclic quadrilateral

Sum of opposite angles of quadrilateral = ${180}^{\circ }$

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

$\angle$B + $\angle$D = ${180}^{\circ }$

= cosA + cos B + cosC + cosD

= cosA + cosB + cos (180-A) + cos(180-B)

= cosA + cosB + (-cosA) + (-cosB)

= cosA + cosB - cosA - cosB

= 0