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The equation $2 \cos^{2} (\frac{x}{2}) \sin^{2} x = x^{2} + \frac{1}{x^{2}}, 0 \leq x \leq \frac{π}{2}$ has

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Correct option is B

Since x2+x−2≥2 and 2cos2x2sin2x≤2⇒2cos2x2sin2x=2 ⇒cos2x2sin2x=1 ⇒cosx2=sinx=1 which is not possible for any choice of x.

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The equation 2cos2x2sin2x=x2+1x2,0≤x≤π2has

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The equation $2 \cos^{2} (\frac{x}{2}) \sin^{2} x = x^{2} + \frac{1}{x^{2}}, 0 \leq x \leq \frac{π}{2}$ has