Question

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.

Options

• 0

• 1

• 2(cos B + cos D)

• 2(cos A + cos C)

Answer 1

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = 0.

Explanation:

Since, ABCD is a cyclic quadrilateral.

∴ A + C = 180°

⇒ A = 180° – C

⇒ cos A = cos (180° – C) = – cos C

⇒ cos A + cos C = 0  ......(i)

Also, B + D = 180°

⇒ cos B + cos D = 0  .....(ii)

Adding (i) and (ii), we get

cos A + cos B + cos C + cos D = 0