\(\begin{array}{l}
\cos x = 2\sin x\\
Lai\,\,\,co:\,\,\,{\cos ^2}x + {\sin ^2}x = 1\\
\Leftrightarrow {\left( {2\sin x} \right)^2} + {\sin ^2}x = 1\\
\Leftrightarrow 5{\sin ^2}x = 1\\
\Leftrightarrow {\sin ^2}x = \frac{1}{5}.\\
\Rightarrow M = \sin x.\cos x = 2{\sin ^2}x = 2.\frac{1}{5} = \frac{2}{5}.
\end{array}\)