The total number of solution(s) of the equation 2x + 3tan x = (5π)/(2) in x ∈ [0,2π]is/are equal to

Correct answer: C. 3 2x + 3tan x = (5π)/(2) ⇒ tan x = - (2)/(3)x + (5π)/(6) y = tan x and y = (5π)/(6) - (2x)/(3) Both the graphs meet exactly three times in [0,2π] . Thus, there are 3 solutions.

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The total number of solution(s) of the equation 2x + 3tan x =...

The total number of solution(s) of the equation

2x + 3tan x = \dfrac{5\pi}{2}

x \in \left[0,2\pi\right]is/are equal to

The total number of solution(s) of the equation 2x + 3tan x = (5π)/(2) in x ∈ [0,2π]is/are equal to

Options

A $1$
B $2$
C $3$
D $4$

Correct answer

C. $3$

Step-by-step solution

2x + 3tan x = \dfrac{5\pi}{2} ⇒ tan x = - \dfrac{2}{3}x + \dfrac{5\pi}{6}

y = tan x and

y = \dfrac{5\pi}{6} - \dfrac{2x}{3}

Both the graphs meet exactly three times in

\left[0,2\pi\right] .<br />Thus, there are

solutions.

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