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If ABCD is a cyclic quadrilateral, then the value of cos A + cos B + cos C + cos D is

If ABCD is a cyclic quadrilateral, then the value of cos A + cos B + cos C + cos D is Correct Answer 0

Concept:

Cyclic quadrilateral: Cyclic quadrilateral is a quadrilateral whose all vertices lie on a single circle.

In cyclic quadrilateral, opposite angles of are supplementary or the sum of opposite angles is 180°.

Calculation:

Given: ABCD is a cyclic quadrilateral

Therefore, A + C = 180° and B + D = 180°

⇒ C = 180° - A and D = 180° - B

Now,

cos A + cos B + cos C + cos D

= cos A + cos B + cos (180° - A) + cos (180° - B)

= cos A + cos B - cos A - cos B                             (∵cos (180° - θ) = -cos θ)

= 0

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