Question

The equation $2{\cos }^2\left(x/2\right){\sin }^{2}x=x^2+x^{-2}:0<x\le \pi /2$ has

• A. no real solution
• B. one real solution
• C. more than real solution
• D. two real solution

Answer 1

The correct option is A no real solution

Given equation is $2{\cos }^2\left(\frac{x}{2}\right){\sin }^{2}x=x^2+x^{-2},x\le \frac{\pi }{9}$
$LHS=2{\cos }^2\left(\frac{x}{2}\right){\sin }^{2}x<2$
and $RHS=x^2+\frac{1}{x^2}\ge 2$
$\therefore$ The equation has no real solution.