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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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If θ1\theta_1 and θ2\theta_2 be the angle which the lines given by (x2+y2)(cos⁡2θsin⁡2α+sin⁡2θ)=(xtan⁡α−ysin⁡θ)2\left(x^2+y^2\right)\left(\cos ^2 \theta \sin ^2 \alpha+\sin ^2 \theta\right)=(x \tan \alpha-y \sin \theta)^2 make with the axis of xx, then for θ=π6\theta=\frac{\pi}{6}, the value of tan⁡θ1+tan⁡θ2=\tan \theta_1+\tan \theta_2=
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Correct option: B
−83cosec⁡2α-\frac{8}{3} \operatorname{cosec} 2 \alpha
Option B (-83\frac{{8}}{{3}} cosec⁡2α\operatorname{cosec} 2 \alpha) is correct because it represents the sum of the tangents of the angles the lines make with the x-axis, calculated using trigonometric identities and the given equation.

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