\[\begin{array}{l}
a)2\sin 2x + 1 = 0 \Leftrightarrow \sin 2x = - \frac{1}{2} \Leftrightarrow \left[ \begin{array}{l}
2x = - \frac{\pi }{6} + k2\pi \\
2x = \frac{{7\pi }}{6} + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - \frac{\pi }{{12}} + k\pi \\
x = \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.\\
b)5{\cos ^2}x - 12\cos x + 7 = 0 \Leftrightarrow \left[ \begin{array}{l}
\cos x = 1\\
\cos x = \frac{7}{5}\left( {VN} \right)
\end{array} \right. \Leftrightarrow x = k2\pi \\
c)\tan \left( {x + \frac{\pi }{4}} \right) - 1 = 0 \Leftrightarrow \tan \left( {x + \frac{\pi }{4}} \right) = 1 \Leftrightarrow x + \frac{\pi }{4} = \frac{\pi }{4} + k\pi \Leftrightarrow x = k\pi
\end{array}\]
