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 ?
A. 0
B. 1
C. -1
D. 2
Answer: Option A
Solution(By Examveda Team)
∠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
Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
Join The Discussion