Answer     $5$

The function $\cos\frac{x}{2}$ has a period of $4\pi$ and strictly decreases from $1$ to $-1$ in the said domain.

The function $\tan 2x$ has a period of $\frac{\pi}{2}$ and, within each period, strictly increase from negative infinity to positive infinity.

Then drawing a graph of both function will reveal there are $5$ intersection points.