In any triangle, show that alb cos C-C cos B] = 62-c?.
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Solution :
We know, cosA=b2+c2−a22bc,cosB=c2+a2−b22ca,cosC=a2+b2−c22ab
∴L.H.S.=a(bcosC−ccosB)=a(b⋅a2+b2−c22ab−c⋅c2+a2−b22ca)
=12(a2+b2−c2−c2−a2+b2)=12(2b2−2c2)
=b2−c2=R.H.S.
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