Phương trình $(sin x + 1)(2\cos 2x - \sqrt 2 ) = 0$ có nghiệm là
A. $x = - \frac{\pi }{2} + k2\pi ,k \in \mathbb{Z}$.
B. $x = - \frac{\pi }{8} + k\pi ,k \in \mathbb{Z}$.
C. $x = \frac{\pi }{8} + k\pi ,k \in \mathbb{Z}$.
D. Cả A, B, C đều đúng.
A. $x = - \frac{\pi }{2} + k2\pi ,k \in \mathbb{Z}$.
B. $x = - \frac{\pi }{8} + k\pi ,k \in \mathbb{Z}$.
C. $x = \frac{\pi }{8} + k\pi ,k \in \mathbb{Z}$.
D. Cả A, B, C đều đúng.
Chọn D.
$(\sin x + 1)(2\cos 2x - \sqrt 2 ) = 0 \Leftrightarrow \left[ \begin{array}{l}\sin x = - 1\\\cos 2x = \frac{{\sqrt 2 }}{2}\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{2} + k2\pi \\2x = \pm \frac{\pi }{4} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{2} + k2\pi \\x = \pm \frac{\pi }{8} + k\pi \end{array} \right.(k \in \mathbb{Z})$
$(\sin x + 1)(2\cos 2x - \sqrt 2 ) = 0 \Leftrightarrow \left[ \begin{array}{l}\sin x = - 1\\\cos 2x = \frac{{\sqrt 2 }}{2}\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{2} + k2\pi \\2x = \pm \frac{\pi }{4} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{2} + k2\pi \\x = \pm \frac{\pi }{8} + k\pi \end{array} \right.(k \in \mathbb{Z})$
