Question

If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.

Options

• 2(cos A + cos C)

• 2(cos A + cos B)

• 2(cos A + cos D)

• 0

Answer 1

If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to 0.

Explanation:

Given that, ABCD is a cyclic quadrilateral.

So, A + C = 180°

`\implies` A = 180° – C

`\implies` cos A = cos(180° – C) = – cos C

`\implies` cos A + cos C = 0  ...(i)

Similarly, cos B + cos D = 0  ...(ii)

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