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If A, B, C, D be the angles of acyclic q...

If `A, B, C, D` be the angles of acyclic quadrilateral, show that : `cosA +cosB+cosC+cosD=0`.

A

2(cosA+cosC)

B

2(cosA+cosB)

C

2(cosA+cosD)

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Given that, ABCD is a cyclic quadrilateral.
So, `A+C=180^(@)`
`implies A=180^(@)-C`
`impliescosA=cos(180^(@)-C)=-cosC`
`implies cosA+cosC=0" ... (i)"`
Similarly, `cosB+cosD=0" … (ii)"`
Adding, `cosA+cosB+cosC+cosD=0`
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