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For any triangle ABC, prove thata(bcosC-...

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

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We know, `cos A = (b^2+c^2-a^2)/(2bc), cosB = (c^2+a^2-b^2)/(2ca), cos C = (a^2+b^2-c^2)/(2ab)`
`:. L.H.S. = a(bcosC-c cosB) = a(b*(a^2+b^2-c^2)/(2ab)-c*(c^2+a^2-b^2)/(2ca))`
`=1/2(a^2+b^2-c^2-c^2-a^2+b^2) = 1/2(2b^2-2c^2)`
`=b^2-c^2 = R.H.S.`
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