Question

if A,B,C,D are the angle of cyclic quadrilateral,then cosA+cosB+cosC+cosD

Answer 1

Since it is a cyclic quadrilateral means that sum of opposite pairs of angles is 180meaning A+C=B+D=180Now,cosA+cosB+cosC+cosD=(cosA+cosC)+(cosB+cosD)=2cos(A+C/2)cos(A-C/2)+2cos(B+D/2)cos(B-D/2)=2cos(180/2)cos(A-C/2)+2cos(180/2)cos(B-D/2)=2cos(90)cos(A-C/2)+2cos(90)cos(B-D/2)=0

Answer 2

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