If the A B C and D are the angles of a cyclic quadrilateral the value of cosA cosB cosC cosD is ........

Quantitative Aptitude ( CCS) Trignometry

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If the A, B, C and D are the angles of a cyclic quadrilateral, the value of cosA+cosB+cosC+cosD is,

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Explanation:

For a cyclic quadrilateral ABCD, opposite angles sum up to 1800 so that,
cosA=cos(180−C)=−cosC, and
cosB=cos(180−D)=−cosD.
So,
cosA+cosB+cosC+cosD=0.
We have used the relation between opposite angles of a cyclic quadrilateral and also the supplementary trigonometric function concepts

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