Let A, B, C, D be the angles of a quadrilateral. If they

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Let A, B, C, D be the angles of a quadrilateral. If they are concyclic, then the value of cos A + cos B + cos C + cos D is

1. 0
2. 1
3. - 1
4. 2

Correct Option: A

ABCD is a concyclic quadrilateral.
∠A + ∠C = ∠B + ∠D = 180°
∴ ∠A = 180° – ∠C
∴ cos A = cos (180° – C) = – cos C
and cos B = – cos D
∴ cos A + cos B + cos C + cos D
= cos A + cos B – cos A – cos B = 0