Show that: `sinAsin(B-C)+sinB sin(C-A)+sinCsin(A-B)=0`

In any triangle ABC, prove that : a sin (B -C) + b sin (C -A) +c sin (A-B) = 0 .

In any triangle ABC, prove that : a^3 sin (B-C)+ b^3 sin (C-A)+ c^3 sin (A-B)=0 .

If A,B and C are the angle of a triangle show that |{:(sin2A,sinC,sinB),(sinC,sin2B,sinA),(sinB,sinA,sin2C):}|=0.

Show that Rr (sin A+sin B + sin C) =Delta

If A + B + C =180^@ , prove that : sin (B+C-A) + sin(C+ A-B)+ sin(A +B-C)=4sin A sinB sinC .

In any triangle A B C , prove that: (a^2sin(B-C))/(sinB+sin C)+(b^2sin(C-A))/(sinC+sin A)+(c^2sin(A-B))/(sinA+sin B)=0

If A, B, C are angles of triangle ABC and a, b, c are lengths of the sides opposite to A, B, C respectively, then show that : a (sin B - sin C)+ b (sin C- sin A)+c (sin A -sin B)= 0 .

Prove that : 2 cosA sinB = sin (A + B)- sin (A - B) .

If A + B + C =180^@ , prove that : sin (B + 2C) + sin (C + 2A) + sin (A + 2B) = 4 sin frac (B-C)(2) sin frac (C-A)(2) sin frac (A-B)(2) .

If A + B + C =pi , prove that : (sin A + sin B +sin C)/(sin A + sin B -sin C)= cot frac (A)(2) cot frac (B)(2) .