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If asintheta="bsin"(theta+(2pi)/3)="csin...

If `asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(2pi)/3)` , prove that `a b+b c+c a=0.`

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Verified by Experts

`asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(2pi)/3)=k`
So,
`Sintheta=k/a`
`sin(theta+(2pi)/3)=k/b`
`sin(theta+(2pi)/3)=k/c`
So,
`=>k/a+k/b+k/c=>sintheta+sin(theta+(2pi)/3)+sin(theta+(2pi)/3)`
...
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