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The number of solutions of $2 \sin^{2} \frac{x}{2} \sin^{2} x = x^{2} + \frac{1}{x^{2}}$ for $0 < x \leq \frac{π}{2}$

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detailed solution

Correct option is D

x2+1x2≥2⇒RHS≥2But LHS=2sin2x2.sin2x<2∴ given equation is not possible

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The number of solutions of 2sin2x2sin2x=x2+1x2 for 0<x≤π2

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The number of solutions of $2 \sin^{2} \frac{x}{2} \sin^{2} x = x^{2} + \frac{1}{x^{2}}$ for $0 < x \leq \frac{π}{2}$