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In any triangle A B C , prove that follo...

In any triangle `A B C` , prove that following: `\ (a^2"sin"(B-C))/(sin A)+(b^2"sin"(C-A))/(sin B)+(c^2'sin"(A-B))/(sin C)=0`

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Solution `Rightarrow`

`frac{a^{2} sin (B-c)}{sin A}+frac{b^{2} sin (1-a)}{sin B}+frac{c^{2} sin (A-B)}{sin C}=0`

`L.H.S` `Rightarrow`

By sine rule.

`frac{a}{sin A}=frac{b}{sin B}=frac{c}{sin C}=k` `a=k sin A, b=k `

put in `L.HS.`

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