If a line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through
an angle 15º, then equation of the line in the new position is

Slope of AB $=\frac{1-0}{3-2}=1$

$\Rightarrow \mathrm{\angle }BAX={45}^{\circ }\text{ (Ref. Fig. 16.18) }$

If AC is the new position of the line AB then  $\mathrm{\angle }CAX={45}^{\circ }+ 15º = 60º$

and thus its equation is

$\begin{array}{l}y=\tan {60}^{\circ }(x-2)\\ y=\sqrt{3}(x-2)\Rightarrow \sqrt{3}x-y=2\sqrt{3}\end{array}$