Phương trình ${\sin ^6}x + {\cos ^6}x = \frac{7}{{16}}$ có nghiệm là:
A. $x = \pm \frac{\pi }{3} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
B. $x = \pm \frac{\pi }{4} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
C. $x = \pm \frac{\pi }{5} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
D. $x = \pm \frac{\pi }{6} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
A. $x = \pm \frac{\pi }{3} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
B. $x = \pm \frac{\pi }{4} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
C. $x = \pm \frac{\pi }{5} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
D. $x = \pm \frac{\pi }{6} + k\frac{\pi }{2}$, $k \in \mathbb{Z}$.
Chọn D.
Phương trình $ \Leftrightarrow 1 - \frac{3}{4}{\sin ^2}2x = \frac{7}{{16}}$ $ \Leftrightarrow \frac{5}{8} + \frac{3}{8}\cos 4x = \frac{7}{{16}}$$ \Leftrightarrow \cos 4x = - \frac{1}{2}$
$ \Leftrightarrow 4x = \pm \frac{{2\pi }}{3} + k2\pi $$ \Leftrightarrow x = \pm \frac{\pi }{6} + k\frac{\pi }{2},\left( {k \in \mathbb{Z}} \right)$.
Phương trình $ \Leftrightarrow 1 - \frac{3}{4}{\sin ^2}2x = \frac{7}{{16}}$ $ \Leftrightarrow \frac{5}{8} + \frac{3}{8}\cos 4x = \frac{7}{{16}}$$ \Leftrightarrow \cos 4x = - \frac{1}{2}$
$ \Leftrightarrow 4x = \pm \frac{{2\pi }}{3} + k2\pi $$ \Leftrightarrow x = \pm \frac{\pi }{6} + k\frac{\pi }{2},\left( {k \in \mathbb{Z}} \right)$.