Question

Write the product as a sum.
11sin(x/2)cos(x/4)

Answer 1

forget the 11 for moment and you use
\[\sin(\alpha)\cos(\beta)=\frac{1}{2}(\sin(\alpha +\beta)+\sin(\alpha -\beta))\]

Answer 2

in this case
\[\alpha =\frac{x}{2},\beta=\frac{x}{4}\] so you can write this as
\[\frac{11}{2}(\sin(\frac{3x}{4})+\sin(\frac{x}{4}))\]