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n \sin A+\sin B-\sin C=-4 \cos \frac{A}{2} \cos \frac{B}{2} \sin \frac{C}{2} |
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Answer» A+B+C = piB+C = pi-A sin(B+C) = sin(pi-A)sin(B)cos(C)+cos(B)sin(C) = sin(pi)cos(A)-cos(pi)sin(A)sin(B)cos(C)+cos(B)sin(C) = sin(A)sin(B)cos(C) - sin(A) = -cos(B)sin(C)(sin(B)cos(C) - sin(A))^2 = (-cos(B)sin(C))^2sin^2(B)cos^2(C) + sin^2(A) - 2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C)-2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A) |
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