The equation `2cos^2x/2sin^2x=x^2+x^(-2);0`

Explanation

To solve the equation \( \frac{2 \cos^2 x}{2 \sin^2 x} = x^2 + x^{-2} \), we will analyze both sides of the equation step by step.

### Step 1: Simplify the Left-Hand Side (LHS)
The left-hand side can be simplified as follows:

\[ \frac{2 \cos^2 x}{2 \sin^2 x} = \frac{\cos^2 x}{\sin^2 x} = \cot^2 x \]
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