Question

if ABCD is a cyclic quadrilateral then show that cosA+cosB+ cosC+cosD=0

Answer 1

HERE IS THE SOLUTION;

◆i) By property of cyclic quadrilateral, sum of opposite angles = 180° 

ii) So if ABCD is a cyclic quadrilateral taken in order, then A + C = 180° and B + D = 180° 

=> A = (180 - C) 
=> cos(A) = cos(180 - C) = -cos(C) 
=> cos(A) + cos(C) = 0 ------ (1) 

Similarly it can be shown that cos(B) + cos(D) = 0 ----------- (2) 

Adding (1) & (2): cos(A) + cos(B) + cos(C) + cos(D) = 0


HENCE PROVED



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