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.  

In the same spirit as baharampuri's answer, the equation write $$\frac{\sin ^2(x)}{2}=x^2+\frac{1}{x^2}$$ The lhs is almays $< \frac 12$ while the rhs is $\geq 2$.
For the last point, consider $$y==x^2+\frac{1}{x^2}$$ $$y'=2 x-\frac{2}{x^3}$$ $$y''=2+\frac{6}{x^4}$$ So, $y'=0$ for $x=\pm 1$ and at this point $y=2$. The second derivative test proves that this is a minimum.
