Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
26.2\cos x(1 - \cos 2x) - \sin 2x = 2\sin x - 1\\
\Leftrightarrow 4\cos x.si{n^2}x - 2\sin x.\cos x = 2\sin x - 1\\
\Leftrightarrow 2\sin x.\cos x(2\sin x - 1) - (2\sin x - 1) = 0\\
\Leftrightarrow (\sin 2x - 1)(2sinx - 1) = 0\\
27.2\sin x - \sqrt 3 = 0 \Leftrightarrow \sin x = \frac{{\sqrt 3 }}{2} \Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{3} + k2\pi \\
x = \frac{{2\pi }}{3} + k2\pi
\end{array} \right.\\
x \in \left( { - 2\pi ;\frac{{3\pi }}{2}} \right) = > x \in \left\{ {\frac{\pi }{3};\frac{{2\pi }}{3};\frac{{ - 5\pi }}{3};\frac{{ - 4\pi }}{3}} \right\}
\end{array}\]
\[\begin{array}{l}
28.\cos x = \frac{1}{2} = > x = \pm \frac{\pi }{3} + k2\pi \\
x \in \left( { - \pi ;\frac{{5\pi }}{2}} \right) = > C\\
29.2\cos x(1 - \cos 2x) - \sin 2x = 2\sin x - 1\\
\Leftrightarrow 4\cos x.si{n^2}x - 2\sin x.\cos x = 2\sin x - 1\\
\Leftrightarrow 2\sin x.\cos x(2\sin x - 1) - (2\sin x - 1) = 0\\
\Leftrightarrow (\sin 2x - 1)(2sinx - 1) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin 2x = 1\\
\sin x = \frac{1}{2}
\end{array} \right. = > \left[ \begin{array}{l}
x = \frac{\pi }{4} + k\pi \\
x = \frac{\pi }{6} + k2\pi \\
x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.
\end{array}\]
\[\begin{array}{l}
30.\sin x = - \frac{{\sqrt 3 }}{2} = > \left[ \begin{array}{l}
x = - \frac{\pi }{3} + k2\pi \\
x = \frac{{7\pi }}{3} + k2\pi
\end{array} \right.\\
x \in \left( { - 2\pi ;4\pi } \right)
\end{array}\]
=>Nghiệm âm lớn nhất : C
