Find the value of `sin^(-1) (sin 5) + cos^(-1) (cos 10) + tan^(-1) {tan(-6)} + cot^(-1) {cot(-10)}`

Explanation

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

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

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

To find an equivalent angle, we can subtract \( 2\pi \) from \( 5 \):
\[
...