`sinA. sin(A+B)=`

Prove the sinA.sin(B-C) + sinB.sin(C-A) + sinC.sin(A-B) = 0

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

Prove that sinB/sinA=sin(2A+B)/sinA-2cos(A+B)

If A and B are acute angles such that sinA = sin^(2) B,cos^(2) A = 3 cos^(2) B then

Prove that a sinA - b sinB = c sin(A-B)

Show that sinA*sin(B-C)+sinB*sin(C-A)+sinC*sin(A-B)=0 .

If sinA : sinC = sin(A-B): sin(B-C) prove that a^2,b^2,c^2 are in A.P.

If A + B + C = pi , show that cot A + sinA/(sin B sin C) = cot B + sin B/(sin C sin A) = cot C + sin C/(sin A sin B)