Show that the two straight lines $x^2(\tan^2 (\theta)+\cos^2 (\theta))-2xy\tan (\theta)+y^2.\sin^2 (\theta)=0$ make with x axis such that the difference of their tangents is $2$.
My Attempt: $$x^2(\tan^2 (\theta) +\cos^2 (\theta))-2xy\tan (\theta) + y^2 \sin^2 (\theta)=0$$
Let $y-m_1x=0$ and $y-m_2x=0$ be the two lines represented by the above equation. Their combined equation is: $$(y-m_1x)(y-m_2x)=0$$ $$y^2-(m_1+m_2)xy+(m_1m_2)x^2=0$$
How do I proceed further?