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JEE Main 202117 MarchEvening Shift
Exam
JEE Main
Year
2021
Date
17 March
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2021 · 17 March · Evening Shift · Mathematics · Trigonometric Equations

The number of solutions of the equation x + 2 x = (π)/(2) in the...

The number of solutions of the equation x+2tan⁡x=π2x + 2\tan x = \dfrac{\pi}{2} in the interval [0,2π]\left[0, 2\pi\right] is

The number of solutions of the equation x + 2 x = (π)/(2) in the interval [0, 2π] is

Options

  1. A33
  2. B44
  3. C22
  4. D55

Correct answer

A. 33

Step-by-step solution

We have x+2tan⁡x=π2x + 2\tan x = \dfrac{\pi}{2}

⇒2tan⁡x=π2−x⇒ 2\tan x = \dfrac{\pi}{2} - x

⇒tan⁡x=−12x+π4⇒ \tan x = - \dfrac{1}{2}x + \dfrac{\pi}{4}

The graph of the two functions is given as

The number of solutions of the equation x + 2 x = (π)/(2) in the interval [0, 2π] is

It is clear from the graph that the number of solutions of the given equation is3.3 .

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