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For any triangle ABC, prove that a(bcosC...

For any triangle ABC, prove that `a(bcosC-ccosB)=b^2-c^2`

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`a (b cos C - c cos B)`
`=(b cos C + c cos B) (b cos C - c cos B)`
`= b^(2) cos^(2) C - c^(2) cos^(2) B`
`= b^(2)cos^(2) C -c^(2) B`
`= b^(2) - c^(2) - (b^(2) sin^(2) C - c^(2) sin^(2) B)`
`= b^(2) - c^(2)` [as by the sine rule, `b sin C = c sin B`]
Alternativey, using cos B and cos C formulae, we can prove the result
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