Question

Find the expansion of sin(A+B-C).

Answer 1

We know that Sin(A+B) = SinA CosB + CosA SinB 
Therefore Sin(A+B+C) = Sin(A+B)CosC + Cos(A+B)SinC 

Now Sin(A+B) = SinACosB + CosASinC. and 
Cos(A+B) = CosACosB -SinASinC 

Substituting we get 

Sin(A+B+C) = (SinACosB +CosASinB)CosC + (CosACosB -SinASinB)SinC 

= SinACosBCosC + CosASinBCosC + CosACosBSinC - SinASinBSinC

Answer 2

Step-by-step explanation:

sin(A+B)=sinA.cosB+cosA.sinB

sin(A+B-C)=sin((A+B)-C)

so,sin(A+B-C)=sin(A+B).cos(-C)+cos(A+B).sin(-C)

sin(A+B-C)=sin(A+B).cosC-cos(A+B).sinC

=sinA.cosB.cosC+cosA.sinB.cosC

-cosA.cosB.sinC+sinA.sinB.sinC

Hope it helps you....