Write the value of `lim_(x->0)(sqrt(1-cos2x))/x`

Explanation

To solve the limit \( \lim_{x \to 0} \frac{\sqrt{1 - \cos(2x)}}{x} \), we can follow these steps:

### Step 1: Use the identity for \( \cos(2x) \)
We know that \( \cos(2x) = 1 - 2\sin^2(x) \). Therefore, we can rewrite \( 1 - \cos(2x) \) as:
\[ 1 - \cos(2x) = 1 - (1 - 2\sin^2(x)) = 2\sin^2(x) \]

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