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

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

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By sine rule -
` frac{a}{sin A}=frac{b}{sin B}=frac{c}{sin C}=k `
`Rightarrow a=k sin A, b=k sin B, C=k sin C . `
`text { Given, } a^{2} sin (B-c)`
` k^{2} sin ^{2} A sin (B-c)`
`= k^{2} sin A sin A sin (B-C)`
`= k^{2} sin A sin (B+C) sin (B-c)`
...
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