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Answer to Question #2710 in Trigonometry for Abhyuday singh

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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10.05.11, 20:28

As, 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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