Question

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

Answer 1

Answer:

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

Step-by-step explanation:

As we know that  

sin(X+Y)=sin X cos Y+cos X sin Y...eq1

sin(X-Y)=sin X cos Y-cos X sin Y...eq2

cos(X+Y)=cos X cos Y-sin X sin Y...eq3

cos(X-Y)=cos X cos Y+ sin X sin Y...eq4

let X=A-B

Y=C

by using eq1,2,3  and 4

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

=[sin A cos B-cos A sin B]cos C-[cos A cos B+sin A sin B]sin C

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