    Question

# If A, B, C, D are angles of a cyclic quadrilateral , find the value of cosA+cosB+cosC+cosD.

A
0
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B
1
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C
2
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D
1
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Solution

## The correct option is A 0A cyclic quadrilateral is a quadrilateral whose all vertices lie on a single circle.And in a cyclic quadrilateral, the sum of opposite angle is 1800i.e. ∠A+∠C=1800 and ∠B+∠D=1800∴ cosA+cosC=2cos(A+C2)cos(A−C2)cosA+cosC=2cos(18002).cos(A−C2)=2cos900.cos(A−C2)=0(∵cos900=0)cosB+cosD=2cos(B+D2).cos(B−D2) =2cos(18002).cos(B−D2) =2cos900.cos(B−D2) =0 (∵cos900=0)∴ cosA+cosC+cosB+cosD=0Hence proved.  Suggest Corrections  0      Similar questions
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