 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiate each coordinate with respect to the parameter $t$ and use the <chain rule>:
$$
\frac{dy}{dx}=\frac{dy/dt}{dx/dt}
=\frac{\sec^2t}{-\csc^2t}=\boxed{-\tan^2t}.
$$
Both coordinates are defined where $\sin t\ne0$ and $\cos t\ne0$. As a check, $xy=1$ there, so the same <derivative> is $-1/x^2$.

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