The angle of rotation of the axes so that the equation $\sqrt{3}x-y+5=0$ may be reduced to the form $y=$ constant is

$\theta =?$;$\sqrt{3}x-y+5=0\cdots \cdots \cdots \left(1\right)$(in old coordinates)

It is reduced to the form $y=\text{constant}\cdots \cdots \cdots \left(2\right)$

$x=X\cos \theta -Y\sin \theta ,y=X\sin \theta +Y\cos \theta$ in equation (1),

We get $\sqrt{3}(X\cos \theta -Y\sin \theta )-(X\sin \theta +\cos \theta )+5=0\cdots \cdots \cdots \left(3\right)$

Equation $\left(2\right)\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\left(3\right)$ represents same equation

$\Rightarrow$Coefficient of X is $=0\Rightarrow \sqrt{3}\cos \theta -\sin \theta =0$

$\Rightarrow \frac{\sqrt{3}}{2}.\cos \theta -\frac{1}{2}\sin \theta =\frac{0}{2}$

$\Rightarrow \sin 60°.\cos \theta -\cos 60°.\sin \theta =0\Rightarrow \sin (60°-\theta )=\sin 0°$

$\Rightarrow 60°-\theta =0°\Rightarrow \theta =60°=\frac{\pi }{3}$