IF A,B,C,D BE ANGLES OF A CYCLIC QUADRILATERAL TAKEN IN ORDER THEN COS A +COS B+ COS C +COS D =0

Asked by Vivek Sehgal | 2nd May, 2012, 01:16: PM

Expert Answer:

Since it is a cyclic quadrilateral means that sum of opposite pairs of angles is 180
meaning 
A+C=B+D=180
Now,
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


 

Answered by  | 2nd May, 2012, 10:35: PM

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