Prove that `tan(cot^(-1)x)=cot(tan^(-1)x)`

Explanation

To prove that \( \tan(\cot^{-1} x) = \cot(\tan^{-1} x) \), we will start by using the definitions of the inverse trigonometric functions and some fundamental identities.

**Step 1: Define the angles.**
Let \( \theta = \cot^{-1} x \). By the definition of the cotangent inverse, we have:
\[ \cot \theta = x \]
This implies that:
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