\(cos2x=-\dfrac{1}{4}\) \(\left(1\right)\)
Vì \(cos2x< 0\Leftrightarrow\dfrac{\pi}{2}< 2x< \dfrac{3\pi}{2}\Leftrightarrow\dfrac{\pi}{4}< x< \dfrac{3\pi}{4}\)
\(\left(1\right)\Leftrightarrow2cos^2x-1=-\dfrac{1}{4}\)
\(\Leftrightarrow2cos^2x=\dfrac{3}{4}\)
\(\Leftrightarrow cos^2x=\dfrac{3}{8}\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=\dfrac{\sqrt[]{6}}{4}\left(\dfrac{\pi}{4}< x< \dfrac{\pi}{2}\right)\\cosx=-\dfrac{\sqrt[]{6}}{4}\left(\dfrac{\pi}{2}< x< \dfrac{3\pi}{4}\right)\end{matrix}\right.\)
- Với \(cosx=\dfrac{\sqrt[]{6}}{4}\Leftrightarrow x=\pm arccos\left(\dfrac{\sqrt[]{6}}{4}\right)+k2\pi\)
- Với \(cosx=-\dfrac{\sqrt[]{6}}{4}\Leftrightarrow x=\pm arccos\left(-\dfrac{\sqrt[]{6}}{4}\right)+k2\pi\)
