Convert to Rectangular Form r^2cos(2theta)=1

$r^{2} \cos (2 θ) = 1$

Divide each term by $\cos (2 θ)$ and simplify.

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Divide each term in $r^{2} \cos (2 θ) = 1$ by $\cos (2 θ)$ .

$\frac{r^{2} \cos (2 θ)}{\cos (2 θ)} = \frac{1}{\cos (2 θ)}$

Cancel the common factor of $\cos (2 θ)$ .

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Cancel the common factor.

$\frac{r^{2} \cos (2 θ)}{\cos (2 θ)} = \frac{1}{\cos (2 θ)}$

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{1}{\cos (2 θ)}$

Convert from $\frac{1}{\cos (2 θ)}$ to $\sec (2 θ)$ .

$r^{2} = \sec (2 θ)$

Take the $square$ root of both sides of the $equation$ to eliminate the exponent on the left side.

$r = \pm \sqrt{\sec (2 θ)}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$r = \sqrt{\sec (2 θ)}$

Next, use the negative value of the $\pm$ to find the second solution.

$r = - \sqrt{\sec (2 θ)}$

The complete solution is the result of both the positive and negative portions of the solution.

$r = \sqrt{\sec (2 θ)}$

$r = - \sqrt{\sec (2 θ)}$

$r = \sqrt{\sec (2 θ)}$

$r = - \sqrt{\sec (2 θ)}$

Convert to Rectangular Form r^2cos(2theta)=1

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