If a triangle

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If a triangle ABCABC, inscribed in a fixed circle, is varied slightly so that its vertices always remain on the circle, show that dacos⁡A+dbcos⁡B+dccos⁡C=0,\frac{da}{\cos A}+\frac{db}{\cos B}+\frac{dc}{\cos C}=0, where a,b,ca,b,c are the side lengths opposite A,B,CA,B,C, respectively.

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