AMC 12 2020a Problem 9

How many solutions does the equation $\tan{(2x)} = \cos{(\tfrac{x}{2})}$ have on the interval $[0, 2\pi]?$

$\textbf{(A) } 1 \textbf{(B) } 2 \textbf{(C) } 3 \textbf{(D) } 4 \textbf{(E) } 5$