If `x in [-1, 0]`, then find the value of `cos^(-1) (2x^(2) - 1) - 2 sin^(-1) x`

Explanation

To solve the expression \( \cos^{-1}(2x^2 - 1) - 2 \sin^{-1}(x) \) for \( x \in [-1, 0] \), we can follow these steps:

### Step 1: Substitute \( x \) with \( \cos \theta \)
Let \( x = \cos \theta \). Given that \( x \in [-1, 0] \), it follows that \( \theta \) will range from \( \frac{\pi}{2} \) to \( \pi \).

### Step 2: Rewrite the expression
Substituting \( x \) into the expression gives us:
\[
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