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In any triangle A B C prove that: sin((B...

In any triangle `A B C` prove that: `sin((B-C)/2)=((b-c)/a)cosA/2`

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`frac{b-c}{2}cos(frac{A}{2})=(frac{ksinB-ksinC}{ksinA})cos frac{A}{2}`
`=>frac{sin B-sin C}{sin A} cos frac{A}{2}`
`=frac{2(cosfrac{B+C}{2})sin(frac{B-C}{2})}{2sin frac{A}{2}cos frac{A}{2}}`
`=frac{cos(frac{pi}{2}-frac{A}{2})sin(frac{B-C}{2})}{sin frac{A}{2}}`
`=frac{sin frac{A}{2}sin frac{B-C}{2}}{sin frac{A}{2}}=sin(frac{B-C}{2})`
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