$\begin{array}{l}
2{\cos ^2}x + \sin x - 1 = 0\\
\Leftrightarrow 2\left( {1 - {{\sin }^2}x} \right) + \sin x - 1 = 0\\
\Leftrightarrow - 2{\sin ^2}x + \sin x + 1 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = 1\\
\sin x = - \frac{1}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{2} + k2\pi \\
x = - \frac{\pi }{6} + k2\pi \\
x = \frac{{7\pi }}{6} + k2\pi
\end{array} \right.\\
Cho\,0 < \frac{\pi }{2} + k2\pi < 6\,tim\,k.\\
Cho\,0 < - \frac{\pi }{6} + k2\pi < 6\,tim\,k.\\
Cho\,0 < \frac{{7\pi }}{6} + k2\pi < 6\,tim\,k.\\
Tu\,do\,ket\,luan\,ban\,nhe!
\end{array}$
