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Radon222 (166)

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Olaaa!! Perrrfect answer. 26  [44 rates]

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a3cos(B-C)=a2ksinAcos(B-C)
                =a2ksin(B+C)cos(B-C)
                =a2k(sin2B+sin2C)/2
                =a2k(2sinBcosB+2sinCcosC)/2
                 =a2(b cosC + c cosB)
Similarly,other two terms are b2(c cosC + a cosA) and c2(acosA+bcosB)

adding the three terms we get      ab(acosB+bcosA)+bc(bcosC+ccosB)+ca(ccosA+acosC)
=abc+bca+cab
=3abc
 

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