show that a (b^2+c^2)cos+b(c^2+a^2)cosB+ c(a^2+b^2)cosC=3abc
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Answer:
Step-by-step explanation:
a(b²+c²)cosA+b(c²+a²)cosB+ c(a²+b²)cosC
=ab²CosA + ac²CosA + bc²CosB+ba²CosB+ ca²CosC+ cb²CosC
= ab(bCosA+aCosB) + bc(cCosB+bCosC)+ca(cCosA+aCosC)
= ab(c) + bc(a)+ca(b) (∵ Projection formula)
= 3abc
= R.H.S
Hence proved
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