10: \(\sqrt{3}\cdot tan\left(2x+\dfrac{\Omega}{3}\right)=-3\)
=>\(tan\left(2x+\dfrac{\Omega}{3}\right)=-\sqrt{3}\)
=>\(2x+\dfrac{\Omega}{3}=-\dfrac{\Omega}{3}+k\Omega\)
=>\(2x=-\dfrac{2}{3}\Omega+k\Omega\)
=>\(x=-\dfrac{1}{3}\Omega+\dfrac{k\Omega}{2}\)
11: \(2\sqrt{2}\cdot sin\left(\dfrac{2x+\Omega}{3}\right)=2\)
=>\(sin\left(\dfrac{2x+\Omega}{3}\right)=\dfrac{1}{\sqrt{2}}\)
=>\(\left[{}\begin{matrix}\dfrac{2x+\Omega}{3}=\dfrac{\Omega}{4}+k2\Omega\\\dfrac{2x+\Omega}{3}=\Omega-\dfrac{\Omega}{4}+k2\Omega=\dfrac{3}{4}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2x+\Omega=\dfrac{3}{4}\Omega+k6\Omega\\2x+\Omega=\dfrac{9}{4}\Omega+k6\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{1}{4}\Omega+k6\Omega\\2x=\dfrac{5}{4}\Omega+k6\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{1}{8}\Omega+k3\Omega\\x=\dfrac{5}{8}\Omega+k3\Omega\end{matrix}\right.\)
12: \(2\sqrt{3}\cdot cos\left(3x+\dfrac{\Omega}{3}\right)-3=0\)
=>\(2\sqrt{3}\cdot cos\left(3x+\dfrac{\Omega}{3}\right)=3\)
=>\(cos\left(3x+\dfrac{\Omega}{3}\right)=\dfrac{3}{2\sqrt{3}}=\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}3x+\dfrac{\Omega}{3}=\dfrac{\Omega}{6}+k2\Omega\\3x+\dfrac{\Omega}{3}=-\dfrac{\Omega}{6}+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=\dfrac{\Omega}{6}+k2\Omega-\dfrac{\Omega}{3}=-\dfrac{1}{6}\Omega+k2\Omega\\3x=-\dfrac{\Omega}{6}-\dfrac{\Omega}{3}+k2\Omega=-\dfrac{1}{2}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{1}{18}\Omega+\dfrac{k2\Omega}{3}\\x=-\dfrac{1}{6}\Omega+\dfrac{k2\Omega}{3}\end{matrix}\right.\)
13: \(6\cdot cos\left(4x+\dfrac{\Omega}{5}\right)+3\sqrt{3}=0\)
=>\(6\cdot cos\left(4x+\dfrac{\Omega}{5}\right)=-3\sqrt{3}\)
=>\(cos\left(4x+\dfrac{\Omega}{5}\right)=-\dfrac{3\sqrt{3}}{6}=-\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}4x+\dfrac{\Omega}{5}=\dfrac{5}{6}\Omega+k2\Omega\\4x+\dfrac{\Omega}{5}=-\dfrac{5}{6}\Omega+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=\dfrac{19}{30}\Omega+k2\Omega\\4x=-\dfrac{31}{30}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{19}{120}\Omega+\dfrac{k\Omega}{2}\\x=-\dfrac{31}{120}\Omega+\dfrac{k\Omega}{2}\end{matrix}\right.\)
14: \(cos\left(x-\dfrac{\Omega}{3}\right)=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x-\dfrac{\Omega}{3}=\dfrac{\Omega}{3}+k2\Omega\\x-\dfrac{\Omega}{3}=-\dfrac{\Omega}{3}+k2\Omega\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\Omega+k2\Omega\\x=k2\Omega\end{matrix}\right.\)
