Does the equation $2\cos^2 (x/2) \sin^2 (x/2) = x^2+\frac{1}{x^2}$ have real solution? 
Do the equation
  $$2\cos^2 (x/2) \sin^2 (x/2) = x^2+\frac{1}{x^2}$$
  have any real solutions?

Please help. This is an IITJEE question.
Here $x$ is an acute angle.
I cannot even start to attempt this question. I cannot understand.  

HINT:
We have
$$2\cos^2(x/2)\sin^2(x/2)=\frac12\sin^2x\le \frac12$$
while 
$$x^2+\frac{1}{x^2}\ge 2$$
