Giải pt Sin(pi/3 - x ) + cos(pi/3 - x ) = -1

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