prove using sine rule - 1) sin ( B-C)/2 = b-c/a cos ( A/2)
2)1+cos(A-B) cos C / 1+cos(A-C) cos B = a2+ b2/ a2- c2
3) (b-c)cot (A/2) + (c-a)cot (B/2) + (a-b)cot (C/2) = 0
4) a cos(B-C/2) = (b+c) sin(A/2)
5) c/(a-b) = tan(A/2) + tan(B/2) / tan(A/2) - tan(B/2)
6) a(cos C - cos B) = 2(b-c) cos^2 (A/2)
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Then, a = k sin A, b = k sin B, c = k sin C