Phương trình lượng giác: $2\cos \,x + \sqrt 2 = 0$ có nghiệm là
A. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = \frac{{3\pi }}{4} + k2\pi \end{array} \right.$.
B. $\left[ \begin{array}{l}x = \frac{{3\pi }}{4} + k2\pi \\x = \frac{{ - 3\pi }}{4} + k2\pi \end{array} \right.$.
C. $\left[ \begin{array}{l}x = \frac{{5\pi }}{4} + k2\pi \\x = \frac{{ - 5\pi }}{4} + k2\pi \end{array} \right.$.
D. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = \frac{{ - \pi }}{4} + k2\pi \end{array} \right.$.
A. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = \frac{{3\pi }}{4} + k2\pi \end{array} \right.$.
B. $\left[ \begin{array}{l}x = \frac{{3\pi }}{4} + k2\pi \\x = \frac{{ - 3\pi }}{4} + k2\pi \end{array} \right.$.
C. $\left[ \begin{array}{l}x = \frac{{5\pi }}{4} + k2\pi \\x = \frac{{ - 5\pi }}{4} + k2\pi \end{array} \right.$.
D. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = \frac{{ - \pi }}{4} + k2\pi \end{array} \right.$.
Chọn B.
$2\cos \,x + \sqrt 2 = 0 \Leftrightarrow \cos x = - \frac{{\sqrt 2 }}{2} \Leftrightarrow \cos x = \cos \frac{{3\pi }}{4} \Leftrightarrow \left[ \begin{array}{l}x = \frac{{3\pi }}{4} + k2\pi \\x = - \frac{{3\pi }}{4} + k2\pi \end{array} \right.,\left( {k \in \mathbb{Z}} \right)$.
$2\cos \,x + \sqrt 2 = 0 \Leftrightarrow \cos x = - \frac{{\sqrt 2 }}{2} \Leftrightarrow \cos x = \cos \frac{{3\pi }}{4} \Leftrightarrow \left[ \begin{array}{l}x = \frac{{3\pi }}{4} + k2\pi \\x = - \frac{{3\pi }}{4} + k2\pi \end{array} \right.,\left( {k \in \mathbb{Z}} \right)$.