Prove that sin(A+B+C+)cos(B+C)-cos(A+B+C)sin(B+C)=sinA

Answer 1

recall that
sinPcosQ - cosPsinQ = sin(P-Q)

LS = sin(A+B+C+)cos(B+C)-cos(A+B+C)sin(B+C)
= sin((A+B+C) -(B+C))
= sinA
= RS