Find the value of `tan^(-1)(-x)-cot^(-1)(-1/x),x gt0`

Explanation

To find the value of \( \tan^{-1}(-x) - \cot^{-1}(-\frac{1}{x}) \) for \( x > 0 \), we can follow these steps:

### Step 1: Rewrite the Inverse Functions
Using the properties of inverse trigonometric functions, we know that:
- \( \tan^{-1}(-y) = -\tan^{-1}(y) \) for \( y > 0 \)
- \( \cot^{-1}(-y) = \pi - \cot^{-1}(y) \) for \( y > 0 \)

Applying these properties to our expression:
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