Question

The number of the solution to:

$2{\cos }^2\frac{x}{2}.{\sin }^{2}x=x^2+\frac{1}{x^2},0\le x\le \frac{\pi }{2}$

Answer 1

$2\left({\cos }^2\frac{\pi }{2}\right)\left({\sin }^{2}x\right)=x^2+\frac{1}{x^2}\Rightarrow 2\left(0\right){\sin }^{2}x=x^2+\frac{1}{x^2}\Rightarrow x^2+\frac{1}{x^2}=0$

This is not possible for any $x\in R$

Number of solutions $=0$