19. Prove that `sin(A +B) sin(A-B)+sin(B+C)sin(B-C) + sin(C+A) sin(C-A)=0`

In a DeltaABC , prove that : sin3A sin(B-C)+sin3B sin(C-A) + sin3C sin (A-B)=0 .

Prove that: sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-D) = 0

Prove that (sin (A - B))/( sin A sin B ) + ( sin (B -C))/( sin B sin C ) + (sin (C - A))/( sin C sin A) =0

Prove that: ("sin"(A-B))/(sin A sin B)+("sin"(B-C))/(sin B sin C)+("sin"(C-A))/(sin C sin A)=0

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

If A+B+C=pi , Prove that : sin( A/2) + sin( B/2) + sin(C/2) =1 + 4 sin( (B+C)/(4)) sin( (C+A)/(4)) sin( (A+B)/(4))

If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

In triangle ABC, prove that sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sin Asin Bsin Cdot

Show that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0