JEE Math Practice Question

If $$\beta $$ is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos $$\theta $$, $$\sqrt 3 \sin \theta $$) and ($$-$$ 3 sin $$\theta $$, $$\sqrt 3 \,\cos \theta $$); $$\theta \in \left( {0,{\pi \over 2}} \right);$$ then $${{2\,\cot \beta } \over {\sin 2\theta }}$$ is equal to :

1. A.$${2 \over {\sqrt 3 }}$$
2. B.$${1 \over {\sqrt 3 }}$$
3. C.$$\sqrt 2 $$
4. D.$${{\sqrt 3 } \over 4}$$