The angle between the lines represented by y^ | vedclass

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(D) The given equation is $x^2(\cos^2 	heta - 1) - xy \sin^2 	heta + y^2 \sin^2 	heta = 0$. Since $\cos^2 	heta - 1 = -\sin^2 	heta$,the equation

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$\frac{\pi}{2}$

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(D) The given equation is $x^2(\cos^2 	heta - 1) - xy \sin^2 	heta + y^2 \sin^2 	heta = 0$. Since $\cos^2 	heta - 1 = -\sin^2 	heta$,the equation becomes: $-\sin^2 	heta x^2 - \sin^2 	heta xy + \sin^2 	heta y^2 = 0$. Dividing by $-\sin^2 	heta$ (assuming $\sin 	heta 
eq 0$),we get: $x^2 + xy - y^2 = 0$. Comparing this with the general homogeneous equation $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$2h = 1$,and $b = -1$. The condition for the lines to be perpendicular is $a + b = 0$. Here,$a + b = 1 + (-1) = 0$. Therefore,the lines are perpendicular to each other,and the angle between them is $\frac{\pi}{2}$.

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

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