Question

If A, B, C, D are angles of a cyclic quadrilateral, prove
that
cos A + cos B + cos C + cos D=0.
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Answer 1

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If A,B,C and D are angles of a cyclic quadrilateral prove that

cosA+cosB+cosC+cosD=0

ANSWER

Since the quadrilateral ABCD is cyclic, we have

A+C=180

o

;B+D=180

o

Hence, cosA=cos(180

o

−C)=−cosC...(1) and cosB=cos(180

o

−C)=−cosD...(2)

Adding (1) and (2) we get

cosA+cosB=−cosC−cosD

or cosA+cosB+cosC+cosD=0

Answer 2

Answer:

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