If `cos (2 sin^(-1) x) = (1)/(9)`, then find the value of x

Explanation

To solve the equation \( \cos(2 \sin^{-1} x) = \frac{1}{9} \), we will follow these steps:

### Step 1: Let \( \theta = \sin^{-1} x \)
We start by letting \( \theta \) be the angle such that \( \sin \theta = x \). Therefore, we can rewrite the equation as:
\[ \cos(2\theta) = \frac{1}{9} \]

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