Find the value of: `tan^(-1)[2cos(2sin^(-1)1/2)]`

Explanation

To find the value of \( \tan^{-1}[2 \cos(2 \sin^{-1}(1/2))] \), we can follow these steps:

### Step 1: Find \( y = \sin^{-1}(1/2) \)
Let \( y = \sin^{-1}(1/2) \). By definition, this means that \( \sin(y) = 1/2 \).

### Step 2: Determine the angle \( y \)
The angle whose sine is \( 1/2 \) is \( \frac{\pi}{6} \) (or \( 30^\circ \)). Thus, we have:
\[
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