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In Delta ABC, a^(2)(s-a)+b^(2)(s-b)+c^(2...

In `Delta ABC, a^(2)(s-a)+b^(2)(s-b)+c^(2)(s-c)=`

A

`4R Delta(cos A+sin B+cos C)`

B

`4R Delta(sin A+sin B+sin C)`

C

`4R Delta(1+4sin.(A)/(2)sin.(B)/(2)sin.(C )/(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`L.H.S.=(1)/(2)(a^(2)(b+c-a)+b^(2)(c+a-b)+c^(2)(a+b-c))`
`=(1)/(2)(a(b^(2)+c^(2)-a^(2))+b(c^(2)+a^(2)-b^(2))+c(a^(2)+b^(2)-c^(2)))`
`=(1)/(2)(2abc cos A+2abc cos B + 2abc cos C)`
`=abc(1+4 sin.(A)/(2)sin.(B)/(2)sin.(C )/(2))`
`=4R Delta (1+4sin.(A)/(2)sin.(B)/(2)sin.(C )/(2))`
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