However, if the symbolic package knows that cos(a+b) == cos(a)cos(b) - sin(a)sin(b) then it works. Something must be known in advance about the relationship

However, if the symbolic package knows that cos(a+b) == cos(a)cos(b) - sin(a)sin(b) then it works. Something must be known in advance about the relationship between sin and cos for addition, otherwise you cannot go from one to the other (and the basic cos(a)^2+sin(a)^2=1 is not enough for that.