Find the value of `sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}]` .

Explanation

To find the value of \( \sin^{-1} \left[ \cos \left( \sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) \right) \right] \), we can follow these steps:

### Step 1: Evaluate \( \sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) \)

The value of \( \sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) \) corresponds to an angle where the sine is \( -\frac{\sqrt{3}}{2} \). The angle that satisfies this in the range of \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) is:

\[
\sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) = -\frac{\pi}{3}
...