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Consider the problem,
sin2A+sin2B+sin2c=2+2cosA.cosB.cosC
We can write sin2A as,
sin2A=21−cos(2A)
Therefore,
LHS=21−cos(2A)+21−cos(2B)+21−cos(2C)=23−(cos(2A)+cos(2B)+cos(2C))=21(3−(2cos(A+B)cos(A−B)+cos(2C)))C=180−(A+B)cos(C)=cos(180−(A+B))cos(C)=−cos(A+B)
Therefore,
=23−(−2cos(C)cos(A−B)+cos(2C))cos(2C)=2
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