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The equation 2 "cos"^(2)((x)/(2))"sin"^(...

The equation `2 "cos"^(2)((x)/(2))"sin"^(2) x = x^(2) + (1)/(x^(2)), 0 le x le (pi)/(2)` has

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To solve the equation \( 2 \cos^2\left(\frac{x}{2}\right) \sin^2 x = x^2 + \frac{1}{x^2} \) for \( 0 \leq x \leq \frac{\pi}{2} \), we will analyze both sides of the equation step by step. ### Step 1: Analyze the Left-Hand Side (LHS) The left-hand side of the equation is: \[ LHS = 2 \cos^2\left(\frac{x}{2}\right) \sin^2 x \] Using the half-angle identity, we can express \( \cos^2\left(\frac{x}{2}\right) \) as: ...
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