\[\begin{array}{l}
\sin \left( {\frac{\pi }{3} - x} \right) + \cos \left( {\frac{\pi }{3} - x} \right) = - 1\\
\Leftrightarrow \sqrt 2 \sin \left( {\frac{\pi }{3} - x + \frac{\pi }{4}} \right) = - 1\\
\Leftrightarrow \sin \left( {\frac{{7\pi }}{{12}} - x} \right) = - \frac{1}{{\sqrt 2 }}\\
\Leftrightarrow \left[ \begin{array}{l}
\frac{{7\pi }}{{12}} - x = - \frac{\pi }{4} + k2\pi \\
\frac{{7\pi }}{{12}} - x = \frac{{5\pi }}{4} + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{5\pi }}{6} + k2\pi \\
x = - \frac{{2\pi }}{3} + k2\pi
\end{array} \right.\,\,\left( {k \in Z} \right).\\
Ap\,\,dung\,\,cong\,\,thuc:\\
\sin \alpha + \cos \alpha = \sqrt 2 \sin \left( {\alpha + \frac{\pi }{4}} \right)\\
Voi\,\,bai\,\,nay:\,\,\alpha = \frac{\pi }{3} - x.
\end{array}\]
