The values of $x$ for which the tangents to the curves $y=x\cos x,y=\left(\sin x\right)/x$ are parallel to the axis of  $x$ are roots of (respectively) 

Let $y=f\left(x\right)=x\cos x\text{ and }y=g\left(x\right)=$

$\left(\sin x\right)/x\text{. Now }{f}^{\text{'}}\left(x\right)=-x\sin x+\cos x\text{ and }{g}^{\text{'}}\left(x\right)=$

$(x\cos x-\sin x)/x^2$. Since the tangents are parallel to $x$-axis  so $f^{\text{'}}\left(x\right)=0\text{ and }{g}^{\text{'}}\left(x\right)=0$ which is turn give cot $x$ = $x$ and  tan $x$ = $x$ respectively