If `(tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8,` then find `xdot`

Explanation

To solve the equation \((\tan^{-1} x)^2 + (\cot^{-1} x)^2 = \frac{5\pi^2}{8}\), we will follow these steps:

### Step 1: Use the relationship between \(\tan^{-1} x\) and \(\cot^{-1} x\)
We know that:
\[ \tan^{-1} x + \cot^{-1} x = \frac{\pi}{2} \]
From this, we can express \(\cot^{-1} x\) in terms of \(\tan^{-1} x\):
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