Performing Sum to Product identity of trigonometric functions

[Albert Chan]

XCas has trigsimplify, but we had to nudge it to get what we want.

XCas> m := sin(a) + sin(b)
XCas> trigsimplify( m(a=c+g, b=c-g) ) (c=(a+b)/2, g=(a-b)/2)

2 * cos((a-b)/2) * sin((a+b)/2)

XCas> tlin( ans() )

sin(a) + sin(b)