In any triangle ABC, find the value of a sin (B – C) + b sin (C – A) + c sin (A – B).

Question

Philoid · Accepted Answer

Lets consider a equilateral as it is given any triangle,

So Here,

A=B=C=60°

Which implies

sin (B – C)=sin (60-60)

sin 0=0

sin (C-A)=sin(60-60)

sin 0=0

sin (A-B)=sin (60-60)

sin 0=0

Therefore,

The Equation will be,

a sin (B – C)+ b sin (C – A)+ c sin (A – B)

a sin 0+ b sin 0+ c sin 0=0