Đáp án:
Giải thích các bước giải:
$\begin{array}{l}
\left( {1 + \cos 2x} \right) + \sin x + \cos x + 2\sin x\cos x = 0\\
\Leftrightarrow \left( {2{{\cos }^2}x + \cos x} \right) + \left( {\sin x + 2\sin x\cos x} \right) = 0\\
\Leftrightarrow \cos x\left( {2\cos x + 1} \right) + \sin x\left( {2\cos x + 1} \right) = 0\\
\Leftrightarrow \left( {2\cos x + 1} \right)\left( {\cos x + \sin x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2\cos x + 1 = 0\\
\cos x + \sin x = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\cos x = - \frac{1}{2}\\
\sin x = - \cos x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = - \frac{1}{2}\\
\tan x = - 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \pm \frac{{2\pi }}{3} + k2\pi \\
x = - \frac{\pi }{4} + k\pi
\end{array} \right.
\end{array}$
