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JEE Main202117 Mar 2021Evening ShiftMathematicsTrigonometric EquationsActual

The number of solutions of the equation x + 2 tan x = π 2 in the interval 0 , 2 π is

Options

  1. A3
  2. B4
  3. C2
  4. D5

Correct answer

A. 3

Step-by-step solution

We have x + 2 tan x = π 2 ⇒ 2 tan x = π 2 - x ⇒ tan x = - 1 2 x + π 4 The graph of the two functions is given as It is clear from the graph that the number of solutions of the given equation is   3 .

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