If ω is one of the angles between the normals to the ellipse a2x2+b2y2=1 at the point whose eccentric angles are θ and 2π+θ , then prove that sin2θ2cotω=1−e2e2

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If is one of the angles between the normals to the ellipse {{

Question

If $ω$ is one of the angles between the normals to the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ at the point whose eccentric angles are $θ$ and $\frac{π}{2} + θ$ , then prove that $\frac{2 cot ω}{sin 2 θ} = \frac{e ^{2}}{1 - e ^{2}}$

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ω

is one of the angles between the normals to the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

at the point whose eccentric angles are

θ

and

\frac{π}{2} + θ

, then prove that

\frac{2 cot ω}{sin 2 θ} = \frac{e ^{2}}{1 - e ^{2}}

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Question Text

ω

is one of the angles between the normals to the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

at the point whose eccentric angles are

θ

and

\frac{π}{2} + θ

, then prove that

\frac{2 cot ω}{sin 2 θ} = \frac{e ^{2}}{1 - e ^{2}}