Nghiệm của phương trình $2\cos \left( {x - \frac{\pi }{3}} \right) - \sqrt 2 = 0$ trong khoảng $\left( { - \frac{\pi }{2};\frac{\pi }{2}} \right)$ là
A. $\left\{ {\frac{{ - \pi }}{{12}};\frac{{ - 7\pi }}{{12}}} \right\}$.
B. $\left\{ {\frac{{7\pi }}{{12}}} \right\}$.
C. $\left\{ {\frac{\pi }{{12}}} \right\}$.
D. $\left\{ {\frac{\pi }{{12}};\frac{{7\pi }}{{12}}} \right\}$.
A. $\left\{ {\frac{{ - \pi }}{{12}};\frac{{ - 7\pi }}{{12}}} \right\}$.
B. $\left\{ {\frac{{7\pi }}{{12}}} \right\}$.
C. $\left\{ {\frac{\pi }{{12}}} \right\}$.
D. $\left\{ {\frac{\pi }{{12}};\frac{{7\pi }}{{12}}} \right\}$.
Chọn C.
$2\cos \left( {x - \frac{\pi }{3}} \right) - \sqrt 2 = 0 \Leftrightarrow \cos \left( {x - \frac{\pi }{3}} \right) = \frac{{\sqrt 2 }}{2} \Leftrightarrow \left[ \begin{array}{l}x - \frac{\pi }{3} = \frac{\pi }{4} + k2\pi \\x - \frac{\pi }{3} = - \frac{\pi }{4} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{{7\pi }}{{12}} + k2\pi \\x = \frac{\pi }{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)$
$2\cos \left( {x - \frac{\pi }{3}} \right) - \sqrt 2 = 0 \Leftrightarrow \cos \left( {x - \frac{\pi }{3}} \right) = \frac{{\sqrt 2 }}{2} \Leftrightarrow \left[ \begin{array}{l}x - \frac{\pi }{3} = \frac{\pi }{4} + k2\pi \\x - \frac{\pi }{3} = - \frac{\pi }{4} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{{7\pi }}{{12}} + k2\pi \\x = \frac{\pi }{{12}} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)$