If β is one of the angles between the normals to the ellipse, x² + 3y² = 9 at the points (3 cos θ, 3 sin θ) and (- 3 sin θ, 3 cos θ); θ (0,(π)/2); then (2 cot β)/(sin 2θ) is equal to:

Limit, Continuity and Differentiability: JEE Main 2018 Mathematics question

JEE Main 2018 · 15 Apr, Morning shift · Q2766

JEE Main 201815 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

\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 :