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Question #2710

If A+B+C=180 or if A+B+C=π, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0.

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## Comments

Andrew10.05.11, 20:28As, A+B+C = π,

a[sin(π+(2C+A))] + b[sin(π+(2A+B))] + c[sin(π+(2B+C))] = 0

Solving for just first part. Solve similarly for rest.

a[sin(π+(2C+A))] => a sinπ cos(2C+A) + a cosπ sin(2C+A)

As, Cosπ and sinπ both equal zero.

The whole statement is zero.

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