1.

In a cyclic quadrilateral ABCD, the value of `2+sum cos A soc B,` isA. `sin^(2)A+sin^(2)B,` isB. `sin^(2)B+sin^(2),` DC. `sin^(2)A+sin^(2)C`D. `sin^(2)B+sin^(2)C`

Answer» Correct Answer - A
In the cyclin quadrilateral ABCD, we have `A+C=pi=B+D`
`thereforecos A+cosB+cos C+cosD)^(2)=0`
`implies(cosA+cosB+cosC+cosD)^(2)=0`
`impliescos^(2)A+cosB+cosC+cos^(2)D+2sumcosAcosB=0`
`implies2 cos^(2)A+2cos^(2)B+2sumcosAcosB=0`
`" "[becausecosC=-cosA and cosD=-cosB]`
`impliessum cos A cos B=-[cos^(2)A+cos^(2)B]`
`sumcosAcosB=-2+sin^(2)A+sin^(2)B`
`implies2+sumcos A cos B=sin^(2)A+sin^(2)B=sin^(2)C+sin^(2)D.`


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