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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main · Mathematics · Trigonometric Equations

The smallest positive root of the equation x-x=0 lies in the...

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

Options

  1. A(0,π2)\left(0, \frac{\pi}{2}\right)
  2. B(π2,π)\left(\frac{\pi}{2}, \pi\right)
  3. C(π,3π2)\left(\pi, \frac{3 \pi}{2}\right)
  4. D(3π2,2π)\left(\frac{3 \pi}{2}, 2 \pi\right)

Correct answer

C. (π,3π2)\left(\pi, \frac{3 \pi}{2}\right)

Step-by-step solution

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