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