Relating Trigonometry And Rational Functions

Geometry Level 2

2cos2x2sin2x=x2+1x22 \cos^{2}\frac{x}{2} \sin^{2}x = x^{2} + \frac{1}{x^{2}}

where 0xπ20 \leq x \leq \frac{\pi}{2}. What is the number of real root(s) of the above equation?

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