The smallest positive root of the equation $\tan x-x=0$ lies in the interval

The smallest positive root of the equation $\tan x-x=0$ lies in the interval
  1. $\left(0, \frac{\pi}{2}\right)$
  2. $\left(\frac{\pi}{2}, \pi\right)$
  3. $\left(\pi, \frac{3 \pi}{2}\right)$
  4. $\left(\frac{3 \pi}{2}, 2 \pi\right)$

Solution

Here, $\tan x-x=0 \Rightarrow \tan x=x$
Clearly smallest positive root lies in the interval $ \left(\pi, \frac{3 \pi}{2}\right) \text {. } $

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

Practice more Trigonometric Equations questions on Aicharya