2 câu trả lời
\[\begin{array}{l} \,\,\,\,\,\,\,\cos \left( {x - 5} \right) = \frac{{\sqrt 3 }}{2},\,\,\,x \in \left( { - \pi ;\,\,\,\pi } \right)\\ \Leftrightarrow \cos \left( {x - 5} \right) = \cos \frac{\pi }{6}\\ \Leftrightarrow \left[ \begin{array}{l} x - 5 = \frac{\pi }{6} + k2\pi \\ x - 5 = - \frac{\pi }{6} + m2\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{6} + 5 + k2\pi \\ x = 5 - \frac{\pi }{6} + m2\pi \end{array} \right.\,\,\,\,\,\left( {k,\,\,m \in Z} \right)\\ x \in \left( { - \pi ;\,\,\pi } \right) \Rightarrow \left[ \begin{array}{l} - \pi < \frac{\pi }{6} + 5 + k2\pi < \pi \\ - \pi < 5 - \frac{\pi }{6} + m2\pi < \pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} - \frac{{7\pi }}{6} - 5 < k2\pi < \frac{{5\pi }}{6} - 5\\ - \frac{{5\pi }}{6} - 5 < m2\pi < \frac{{7\pi }}{6} - 5 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} - 1,4 < k < - 0,379\\ - 1,2 < m < - 0,2 \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} k = 0\\ m \in \emptyset \end{array} \right. \Rightarrow x = \frac{\pi }{6} + 5. \end{array}\]
