a: \(cos\left(2x+\dfrac{\Omega}{6}\right)=-\dfrac{1}{2}\)
=>\(cos\left(2x+\dfrac{\Omega}{6}\right)=cos\left(-\dfrac{2}{3}\Omega\right)\)
=>\(\left[{}\begin{matrix}2x+\dfrac{\Omega}{6}=-\dfrac{2}{3}\Omega+k2\Omega\\2x+\dfrac{\Omega}{6}=\dfrac{2}{3}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2x=-\dfrac{2}{3}\Omega-\dfrac{\Omega}{6}+k2\Omega=-\dfrac{5}{6}\Omega+k2\Omega\\2x=\dfrac{2}{3}\Omega-\dfrac{\Omega}{6}+k2\Omega=\dfrac{1}{2}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{5}{12}\Omega+k\Omega\\x=\dfrac{1}{4}\Omega+k\Omega\end{matrix}\right.\)
b: \(2\cdot sin\left(\dfrac{x}{2}-\dfrac{\Omega}{4}\right)+\sqrt{3}=0\)
=>\(2\cdot sin\left(\dfrac{x}{2}-\dfrac{\Omega}{4}\right)=-\sqrt{3}\)
=>\(sin\left(\dfrac{1}{2}x-\dfrac{\Omega}{4}\right)=-\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{\Omega}{4}=-\dfrac{\Omega}{3}+k2\Omega\\\dfrac{1}{2}x-\dfrac{\Omega}{4}=\Omega+\dfrac{\Omega}{3}+k2\Omega=\dfrac{4}{3}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\dfrac{1}{2}x=-\dfrac{\Omega}{3}+\dfrac{\Omega}{4}+k2\Omega=-\dfrac{\Omega}{12}+k2\Omega\\\dfrac{1}{2}x=\dfrac{4}{3}\Omega+\dfrac{\Omega}{4}+k2\Omega=\dfrac{19}{12}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{\Omega}{6}+k4\Omega\\x=\dfrac{19}{6}\Omega+k4\Omega\end{matrix}\right.\)
