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In DeltaABC, prove that: bsinB-c sinC=as...

In `DeltaABC`, prove that: `bsinB-c sinC=asin(B-C)`

Text Solution

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LHS `=bsinB-csinC`
`=(ksinB)sinB-(ksinC)sinC` (From sine rule)
`=k(sin^(2)B-sin^(2)C)`
`=ksin(B+C)sin(B-C)`
`ksin(180^(@)-A).sin(B-C)`
`ksinA.sin(B-C)`
`=asin(B-C)`
=RHS Hence proved.
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