1

The set $\{x\in\mathbb R\mid x>0,(1+x^2)\tan2x=x\}$ is

  1. Empty

  2. Finite

  3. Countably infinite

  4. Uncountable

I have plotted the graph and see that the required set is countably infinite. How to prove this fact?

user26857
  • 52,094
vqw7Ad
  • 2,055
  • 2
    Hint : how many solutions the equation $(1+x^2)\tan(2x)=x$ on $\left(-\frac{\pi}{2}+\frac{k\pi}{2},\frac{\pi}{2}+\frac{k\pi}{2}\right)$ where $k\in\mathbb Z$ ? – Surb Mar 11 '21 at 09:53

0 Answers0