[tex]\bf y=x+2cos(x)\qquad \qquad [-2\pi ,2\pi ]\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=1-2sin(x)\implies 0=1-2sin(x)\implies sin(x)=\cfrac{1}{2}
\\\\\\
\measuredangle x=sin^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}
\end{cases}[/tex]
only in the 1st and 2nd quadrants, where sine is positive
