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Question: Answered & Verified by Expert
The smallest positive root of the equation $\tan x-x=0$ lies in
MathematicsTrigonometric Ratios & IdentitiesWBJEEWBJEE 2016
Options:
  • A $\left(0, \frac{\pi}{2}\right)$
  • B $\left(\frac{\pi}{2}, \pi\right)$
  • C $\left(\pi, \frac{3 \pi}{2}\right)$
  • D $\left(\frac{3 \pi}{2}, 2 \pi\right)$
Solution:
2642 Upvotes Verified Answer
The correct answer is: $\left(\pi, \frac{3 \pi}{2}\right)$
Given equation is
$\tan x-x=0$
$\tan x=x$
Solutions are abscissae of points of intersection of the curves $y=\tan x$ and $y=x$. From the figure, it is clearty visible that solution lies in $\left(\pi, \frac{3 \pi}{2}\right)$

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