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If ABCD is a cyclic quadrilateral, then ...

If ABCD is a cyclic quadrilateral, then the value of cosA-cosB+cosC-cosD is equal to

A

0

B

1

C

2(cosB-cosD)

D

2(cosA-cosC)

Text Solution

Verified by Experts

The correct Answer is:
A
We know that, `A+C=180^(@)`,
Since ABCD is a cyclic quadrilateral.
`impliesA=180^(@)-C`
`impliescosA=cos(180^(@)-C)=-cosC`
`impliescosA+cosC=0" ... (i)"`
Now, `B+D=180^(@)`, then
`cosB+cosD=0" ... (ii)"`
Subtracting Eq. (ii) from Eq. (i), we get
`cosA-cosB+cosC-cosD=0`
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