Solve Trigonometry Proof: A+B+C=π

[anthonych414]

Homework Statement

if A+B+C=π, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0

Homework Equations

sin(x-y)=sinxcosy-cosxsiny

The Attempt at a Solution

I tried to expand but to no avail. Any help is appreciated.

 

[NasuSama]

Homework Statement

if A+B+C=π, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0

Homework Equations

sin(x-y)=sinxcosy-cosxsiny

The Attempt at a Solution

I tried to expand but to no avail. Any help is appreciated.

Here are some advices:

→Take A + B + C = π and solve for one of the variables. Then, substitute C, B or A for asin(B-C)+bsin(C-A)+csin(A-B)=0.
→Since you get the shift by π in sine expressions, you need to use these formulas:

sin(x - π) = -sin(x) and sin(-x + π) = sin(x) [Make sure that when get the expression like sin(A + B - π), we have -sin(A + B)]

Oh! This link might help you! http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Symmetry.2C_shifts.2C_and_periodicity

Good luck, and let me know if you have comments or problems. :D