1.
\(\Leftrightarrow cosx=\frac{\sqrt{3}}{2}\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+k2\pi\\x=-\frac{\pi}{6}+n2\pi\end{matrix}\right.\)
Do \(0< x< 2\pi\Rightarrow\left\{{}\begin{matrix}0< \frac{\pi}{6}+k2\pi< 2\pi\\0< -\frac{\pi}{6}+n2\pi< 2\pi\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-\frac{1}{12}< k< \frac{11}{12}\\\frac{1}{12}< n< \frac{13}{12}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}k=0\\n=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}\\x=\frac{11\pi}{6}\end{matrix}\right.\) \(\Rightarrow\sum x=\frac{\pi}{6}+\frac{11\pi}{6}=2\pi\)
2.
\(-\frac{\pi}{4}\le x\le\frac{\pi}{3}\Rightarrow-\frac{\sqrt{2}}{2}\le sinx\le\frac{\sqrt{3}}{2}\)
\(\Rightarrow0\le\left|sinx\right|\le\frac{\sqrt{3}}{2}\)
\(y_{max}=\frac{\sqrt{3}}{2}\) khi \(x=\frac{\pi}{3}\)
\(y_{min}=0\) khi \(x=0\)
1.
\(2cosx-\sqrt{3}=0\\ \Leftrightarrow cosx=\frac{\sqrt{3}}{2}\\ \Leftrightarrow x=\pm\frac{\pi}{6}+k2\pi\left(k\in Z\right)\)
Do: \(0\le x\le2\pi\)
\(\Rightarrow\left\{{}\begin{matrix}0\le\frac{\pi}{6}+k2\pi\le2\pi\\0\le-\frac{\pi}{6}+k2\pi\le2\pi\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}-\frac{1}{12}\le k\le\frac{11}{12}\Rightarrow k=0\\\frac{1}{12}\le k\le\frac{13}{12}\Rightarrow k=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}k=0\Rightarrow x=\frac{\pi}{6}\\k=1\Rightarrow x=\frac{13\pi}{6}\end{matrix}\right.\)
Tổng các nghiệm là: \(\frac{\pi}{6}+\frac{13\pi}{6}=\frac{7\pi}{3}\)