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Question

Show that 1+cos(AB)cosC1+cos(AC)cosB=a2+b2a2+c2

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Solution

1+cos(AB)cosC1+cos(AC)cosB
1cos(AB)cos(A+B)1cos(AC)cos(A+C)
[A+B+C=πso thatcosC=cos(A+B)]
=1(cos2Asin2B)1(cos2Asin2C)
=sin2A+sin2Bsin2A+sin2C=a2+b2a2+c2.
LHS=RHS
Hence proof

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