Em tách ra hỏi từng câu thôi nhé
48)
\(\begin{array}{l}
pt \Leftrightarrow \frac{{1 - \cos 2x}}{2} + \frac{{1 + \cos 6x}}{2} = 1 - {\sin ^2}2x\\
\Leftrightarrow 2 + \cos 6x - \cos 2x = 2 - 2{\sin ^2}2x\\
\Leftrightarrow - 2\sin 4x.\sin 2x = - 2{\sin ^2}2x\\
\Leftrightarrow \sin 4x\sin 2x - {\sin ^2}2x = 0\\
\Leftrightarrow \sin 2x\left( {\sin 4x - \sin 2x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 2x = 0\\
\sin 4x = \sin 2x
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{k\pi }}{2}\\
4x = 2x + k2\pi \\
4x = \pi - 2x + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{k\pi }}{2}\\
x = k\pi \\
x = \frac{\pi }{6} + \frac{1}{3}k\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{k\pi }}{2}\\
x = \frac{\pi }{6} + \frac{1}{3}k\pi
\end{array} \right.\\
\Rightarrow x \in \left\{ {0;\frac{\pi }{2};\pi ;\frac{{3\pi }}{2};2\pi ;\frac{\pi }{6};\frac{{5\pi }}{6};\frac{{7\pi }}{6};\frac{{11\pi }}{6}} \right\}
\end{array}\)
Tổng các nghiệm là \(9\pi\)
