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For any acute angled triangleABC,(sinA)/(A)+(sinB)/(B)+(sinC)/(C ) can

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Solution :Let `f(x)=(sinx)/(x)`
`rarr f(x)=(xcosx-sinx)/(x^(2))=(cosx(x-tanx))/(x^(2))`
`rarr f(X)=(-x^(2)sinx-2xcosx+2 sinx)/(x^(3))`
g(x)=`-x^(2)sinx-2xcosx+2 sinx`
`g(X)=-x^(2)cosxlt0 forall x in (0,pi//2)`
`rarr for xgt0` we have `g(X) lt g(0)i.e g(x)lt0`
`rarr f(X)lt0andf(x)lt0,x in (0,(pi)/(2))`
`rarr f(a+B+C)/(3)gtf(A)+f(B)+f(C )/(3)`
`rarr (SINA)/(A)+(sinB)/(B)+(sinC)/(C )LE(9sqrt(3))/(2PI)=2.5`


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