2022 AMC 12A Problem 12

Let M be the midpoint of \overline{AB} in regular tetrahedron ABCD. What is \cos(\angle CMD)?

\textbf{(A) } \frac14 \qquad \textbf{(B) } \frac13 \qquad \textbf{(C) } \frac25 \qquad \textbf{(D) } \frac12 \qquad \textbf{(E) } \frac{\sqrt{3}}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.