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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

Let f(x) = max\ tan x,cot x\ . Then the number of roots of the...

Let

f\left(x\right) = max\left\{tan x,cot x\right\} .

Then the number of roots of the equation

f \left(

x\right) =

\dfrac{1}{2}in \left(

0,

2\pi\right)is

$Let f(x) = max\ tan x,cot x\ . Then the number of roots of the equation f ( x) = (1)/(2)in ( 0, 2π)is$

Options

A $0$
B $1$
C $2$
D $4$

Correct answer

A. $0$

Step-by-step solution

$Let f(x) = max\ tan x,cot x\ . Then the number of roots of the equation f ( x) = (1)/(2)in ( 0, 2π)is$
From the graph of

\tan x

and

\cot x

, we see that the range of

f

\left(x\right)

is \left[-1,0\right] \cup \left[1, \infty\right) .

Hence,

f\left(x\right) = max\left\{tan x, cot x\right\}

and

g\left(x\right) =

\dfrac{1}{2}do not cut each other

⇒

The number of solutions is zero.

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