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 will solve it step by step.

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

The value of \( \sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) \) corresponds to the angle whose sine is \( -\frac{\sqrt{3}}{2} \). The sine function is negative in the fourth quadrant.

The reference angle for \( \frac{\sqrt{3}}{2} \) is \( \frac{\pi}{3} \) (or 60 degrees). Therefore:

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