(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the place where the parametric curve intersect itself

[tex] x = 1-2cos^{2}t [/tex]

[tex] y = tant(1-2cos^{2}t)[/tex]

2. Relevant equations

3. The attempt at a solution

So I started with the x values..

[tex] 1-2cos^{2}t_{1} = 1-2cos^{2}t_{2} [/tex]

By canceling the same stuff on both sides, I got

[tex] cos^{2}t_{1} = cos^{2}t_{2} [/tex]

Then I tried with y

I rewrote y in a different form.

[tex] y_{1} = tan t (x_{1}) [/tex]

and

[tex]y_{2} = tan t(x_{2}) [/tex]

This is possible since y already contains an expression for x.

Since the curve intersect itself, we know x1 must equal x2 so they cancel out.

then I am left with [tex] tant_{1}= tant_{2} [/tex]

but I can't solve for t

Appreciate any help. Thanks

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# Place where parametric curve itself itself

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