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Question

In any triangle ABC prove that the identities.
sin2A+sin2B+sin2CcosA+cosB+cosC1=8cos(A/2)cos(B/2)cos(C/2).

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Solution

L.H.S. =4sinAsinBsinC4sin(A/2)sin(B/2)sin(C/2)
=8cos(A/2)cos(B/2)cos(C/2) sinA=2sin(A/2)cos(A/2) etc.

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