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

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

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Verified by Experts

On using the sine rule we know,

`a / sin A=b / sin B=c / sin C=k `

`a=k sin A, b=k sin B, c=k sin C`

Let us consider the `LHS`

`a(sin B-sin C)+b(sin C-sin A)+c(sin A-sin B)`

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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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