#### Answer

$$r^2=\sec (2\theta).$$

#### Work Step by Step

We have $$x^2-y^2=1\Longrightarrow r^2\cos^2\theta -r^2\sin^2\theta=1\\
\Longrightarrow r^2(\cos^2\theta -\sin^2\theta)=1\\
\Longrightarrow r^2\cos(2\theta )=1.
$$
Hence, the polar equation of the hyperbola is
$$r^2=\sec (2\theta).$$