the difference of the tangents of the angles made by the lines 3x²-2xy-y²=0 with x-axis is?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{For} {\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0, \mathrm{if} \mathrm{\theta } \mathrm{is} \mathrm{angle} \mathrm{between} \mathrm{lines}, \mathrm{then} \\ \mathrm{tan\theta }=\frac{2\sqrt{{\mathrm{h}}^2-\mathrm{ab}}}{\left|\mathrm{a}+\mathrm{b}\right|} \\ \mathrm{Hence} \mathrm{for} 3{\mathrm{x}}^2-2\mathrm{xy}-{\mathrm{y}}^2=0 \\ \mathrm{tan\theta }=\frac{2\sqrt{{\left(-1\right)}^2-3\times \left(-1\right)}}{\left|3-1\right|}=\frac{2\sqrt{1+3}}{2}=2 \left(\mathrm{Answer}\right) \end{gathered}$$

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