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Question

If A,B,C,D are the angles of a cyclic quadrilateral then cosA+cosB+cosC+cosD=......

A
1
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B
1
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C
±1
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D
0
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Solution

The correct option is D 0
In cyclic quadrilateral sum of opposite angles is 180
A+C=180 & B+D=180
cosA+cosC=2cos(A+C2)cos(AC2)
cosA+cosC=2cos(1802)cos(AC2)
cosA+cosC=0
cosB+cosD=2cos(B+D2)cos(BD2)
cosB+cosD=2cos(1802)cos(BD2)
cosB+cosD=0
cosA+cosB+cosC+cosD=0

1205587_1283427_ans_4bd4acd0f3d7449086129f755f0544ee.jpg

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