if line joining A (2,0) AND B(3,1) is rotated abt A in anticlockwise direction thru an angle 15 . find equation of the line in new position

slope of the line AB = $\frac{1-0}{3-2}=1$
thus the angle made with the x-axis is 45 deg
let after rotation the point B reaches to the point C.
such that $\angle CAB=15$
thus the slope of the line CA be $\tan (45+15)=\tan 60=\sqrt{3}$
the coordinates of the point A are (2,0)
therefore the equation of the line CA is:
$$\begin{gathered} y-0=\sqrt{3}(x-2) \\ \sqrt{3}x-y=2\sqrt{3} \end{gathered}$$

hope this helps you