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For any triangle ABC, prove that (sin(B-...

For any triangle ABC, prove that `(sin(B-C)/(sin(B+C)=(b^2-c^2)/(a^2)`

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Verified by Experts

By sine rule,
`a/(sinA)= b/(sinB) = c/(sinC)=k` (say)
`therefore a=k sinA, b=k sinB` and `c=k sinC`
LHS `=(b^(2)-c^(2))/(a^(2)) = (k^(2)sin^(2)B-k^(2)sin^(2)C)/(k^(2)sin^(2)A)`
`=(sin^(2)B-sin^(2)C)/(sin^(2)A)`
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AAKASH INSTITUTE ENGLISH-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
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