[" सदिश विधि से सिद्ध करें कि किसी "/_4BC" में "],[(a)/(sin A)=(b)/(sin B)=(c)/(sin C)]

a sin A-b sin B=c sin(A-B)

a sin A-b sin B=c sin(A-B)

If a,b,c are the lengths of sides,BC,CA and AB of a triangle ABC, prove that vec BC+vec CA+vec AB=vec O and deduce that (a)/(sin A)=(b)/(sin B)=(c)/(sin C) .

b sin Bc sin C = a sin (BC)

(cos A)/(sin B sin C)+(cos B)/(sin C sin A)+(cos C)/(sin A sin B)=2

sin A + sin B-sin C = 4sin ((A) / (2)) sin ((B) / (2)) cos ((C) / (2))

If (b+c)/(5)=(c+a)/(6)=(a+b)/(7) then sin A:sin B:sin C=4:3:2

sin (B + CA) + sin (C + AC) + sin (A + BC) = 4sin A sin B sin C

Prove that (a ^ (2) sin (BC)) / (sin B + sin C) + (b ^ (2) sin (CA)) / (sin C + sin A) + (c ^ (2) sin ( AB)) / (sin A + sin B) = 0