Answer
If this equation has no solution over the interval $[0,2\pi)$, we can conclude that the graph of $~~y = cot~\frac{x}{2}-csc~\frac{x}{2} - 1~~$ does not cross the x-axis over this interval.
We can see that the graph of $~~y = cot~\frac{x}{2}-csc~\frac{x}{2} - 1~~$ does not cross the x-axis over the interval $[0, 2\pi)$
Work Step by Step
$cot~\frac{x}{2}-csc~\frac{x}{2} - 1 = 0$
If this equation has no solution over the interval $[0,2\pi)$, we can conclude that the graph of $~~y = cot~\frac{x}{2}-csc~\frac{x}{2} - 1~~$ does not cross the x-axis over this interval.
We can graph $~~y = cot~\frac{x}{2}-csc~\frac{x}{2} - 1~~$ to confirm this.
We can see that the graph of $~~y = cot~\frac{x}{2}-csc~\frac{x}{2} - 1~~$ does not cross the x-axis over the interval $[0, 2\pi)$
