Answer
$csc~x-cot~x = tan~\frac{x}{2}$
Work Step by Step
$csc~x-cot~x$
When we graph this function, it looks like the graph of $~~tan~\frac{x}{2}$
We can verify this algebraically:
$csc~x-cot~x$
$=\frac{1}{sin~x}-\frac{cos~x}{sin~x}$
$=\frac{1-cos~x}{sin~x}$
$=tan~\frac{x}{2}$
