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SinA+sinB+sinC=0,cosA+cosB+cosC=0 then prove that A-B=2pi/3, B-C=2pi/3, C-A=2pi/3

SinA+sinB+sinC=0,cosA+cosB+cosC=0 then prove that A-B=2pi/3, B-C=2pi/3, C-A=2pi/3

Grade:12

1 Answers

Amit Nardiya
askIITians Faculty 24 Points
8 years ago
Let us consider 3 complex numbers
a= cos A + i sin A, b= cos B + i sin B, c= cos C + i sin C,
Since cos A + cos B + cos C = 0 = sin A + sin B + sin C


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Thanks & Regards,
Amit Nardiya,
askIITians faculty.

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