If A, B and C are the angles of a triangle, then sin(B + C − A) equals:

$B+C=180$° − A, so $B+C-A=180$° − $2A$, and sin(180° − $x$) = sinx gives sin$(B+C-A)=$ sin2A. Check with $A=50$°, $B=60$°, $C=70$°: sin(60° + 70° − 50°) = sin80° = 0.985 and sin100° = 0.985 as well. The sign flip belongs to cosine, not sine.