Find the value of `sin^(-1)(sin5)+cos^(-1)(cos10)+tan^(-1){tan(-6)}+cot^(-1){cot(-10)}dot`

Explanation

To solve the expression \( \sin^{-1}(\sin 5) + \cos^{-1}(\cos 10) + \tan^{-1}(\tan(-6)) + \cot^{-1}(\cot(-10)) \), we will simplify each term step by step.

### Step 1: Simplifying \( \sin^{-1}(\sin 5) \)

The function \( \sin^{-1}(x) \) is defined in the range \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \). Since \( 5 \) is outside this range, we need to find an equivalent angle within the range.

We can express \( 5 \) in terms of \( 2\pi \):
\[
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