Question

If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.

Options

• 0

• 1

• 2(cos B – cos D)

• 2(cos A – cos C)

Answer 1

If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to 0.

Explanation:

We know that, A + C = 180°

Since ABCD is a cyclic quadrilateral.

`\implies` A = 180° – C

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

`\implies` cos A + cos C = 0  ...(i)

Now, B + D = 180°, then

cos B + cos D = 0  ...(ii)

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

cos A – cos B + cos C – cos D = 0