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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NTA Abhyas 2020 · 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).<br />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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