\(\dfrac{\Omega}{2}< a< \Omega\)
=>\(cosa< 0\)
\(sin\alpha=\dfrac{1}{3}\)
\(\Leftrightarrow cos^2\alpha=1-sin^2\alpha=1-\left(\dfrac{1}{3}\right)^2=\dfrac{8}{9}\)
mà cosa<0
nên \(cos\alpha=-\dfrac{2\sqrt{2}}{3}\)
\(cos\left(\alpha-\dfrac{\Omega}{6}\right)=cos\alpha\cdot cos\left(\dfrac{\Omega}{6}\right)+sin\alpha\cdot sin\left(\dfrac{\Omega}{6}\right)\)
\(=-\dfrac{2\sqrt{2}}{3}\cdot\dfrac{\sqrt{3}}{2}+\dfrac{1}{3}\cdot\dfrac{1}{2}\)
\(=\dfrac{-2\sqrt{6}+1}{6}\)