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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 ?

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 ? Correct Answer 0

Trigonometry mcq solution image
∠A + ∠C = ∠B + ∠D = 180°
∴ ∠A = 180° - ∠C
cosA = cos(180° - C) ⇒ -cosC
Similarly,
cosB = -cosD
⇒ cosA + cosB + cosC + cosD
⇒ cosA + cosB - cosA - cosB = 0
Alternate Solution :
Put, A = B = C = D = 90°
= cosA + cosB + cosC + cosD
= cos90° + cos90° + cos90° + cos90°
= 0 + 0 + 0 + 0
= 0

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