\(y=2cos\left(x-\frac{\pi}{6}\right).cos\frac{\pi}{6}=\sqrt{3}cos\left(x-\frac{\pi}{6}\right)\)
Mà \(-1\le cos\left(x-\frac{\pi}{6}\right)\le1\)
\(\Rightarrow-\sqrt{3}\le y\le\sqrt{3}\)
\(y_{min}=-\sqrt{3}\) khi \(cos\left(x-\frac{\pi}{6}\right)=-1\)
\(y_{max}=\sqrt{3}\) khi \(cos\left(x-\frac{\pi}{6}\right)=1\)
\(y=cosx+cos\left(x-\frac{\pi}{3}\right)\\ =cosx+\frac{1}{2}cosx+\frac{\sqrt{3}}{2}sinx\\ =\frac{3}{2}cosx+\frac{\sqrt{3}}{2}sinx\\ \Rightarrow y^2\le\left(\frac{3^2}{2^2}+\frac{3}{2^2}\right)\left(sin^2x+cos^2x\right)=3\\ \Rightarrow-\sqrt{3}\le y\le\sqrt{3}\)
\(\Rightarrow Max\text{ }Y=\sqrt{3}\Leftrightarrow\frac{3}{2}cosx+\frac{\sqrt{3}}{2}sinx=\sqrt{3}\\ Max\text{ }Y=-\sqrt{3}\Leftrightarrow\frac{3}{2}cosx+\frac{\sqrt{3}}{2}sinx=-\sqrt{3}\)
