Answer
$csc(x)$,
$2csc(\frac{1}{2}x)$.
See graph.
Work Step by Step
Step 1. Given $f(x)=\frac{1}{2}x$ and $g(x)=2csc(x)$, we have $(f\circ g)(x)=f(g(x))=\frac{1}{2}(2csc(x))=csc(x)$,
Step 2. We have $(g\circ f)(x)=g(f(x))=2csc(\frac{1}{2}x)$.
Step 3. See graph.