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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#339914 on Dec 2023
#339914 on Dec 2023
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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.