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Prove that: sinAsin(B-C)+sinBsin(C-A)+...

Prove that:
`sinAsin(B-C)+sinBsin(C-A)+sinCsin(A-B)=0`

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In DeltaABC if sinA.sin(B-C)= sinC.sin(A-B),then-(A!=B!=C) (A) tanA, tanB, tanC are in arithmetic progression (B) cotA, cotB, cotC are in arithmetic progression (C) cos2A, cos2B, cos2C are in arithmetic progression (D) sin2A. sin2B. sin2C are in arithmetic progression