Question

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

• A. $\left(0, \frac{\pi}{2}\right)$
• B. $\left(\frac{\pi}{2}, \pi\right)$
• C. $\left(\pi, \frac{3 \pi}{2}\right)$
• D. $\left(\frac{3 \pi}{2}, 2 \pi\right)$

Answer 1

Answer: (C)

Here, $\tan\, x-x=0$
$ \Rightarrow \,\tan x=x$

Clearly smallest positive root lies in the interval $\left(\pi, \frac{3 \pi}{2}\right)$