Answer
$\frac{11}{2}(\sin\frac{3x}{4}+\sin\frac{x}{4})$
Work Step by Step
Use the first Product-to-Sum Formula, $\sin u\cos v=\frac{1}{2}[\sin(u+v)+\sin(u-v)]$.
$11\sin\frac{x}{2}\cos\frac{x}{4}$
$=11\times\frac{1}{2}[\sin(\frac{x}{2}+\frac{x}{4})+\sin(\frac{x}{2}-\frac{x}{4})]$
$=\frac{11}{2}(\sin\frac{3x}{4}+\sin\frac{x}{4})$