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

Explanation

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

### Step 1: Analyze the Left-Hand Side (LHS)

The LHS is given by:
\[ LHS = 2 \cos^2 \left(\frac{x}{2}\right) \sin^2 x \]
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