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JEE Main 202118 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2021 · 18 March · Morning Shift · Mathematics · Trigonometric Equations

The number of solutions of the equation | x | = x + (1)/( x) in the...

The number of solutions of the equation ∣cot⁡x∣=cot⁡x+1sin⁡x| \cot x | = \cot x + \dfrac{1}{\sin x} in the interval [0,2π][ 0, 2\pi ] is

Correct answer

1

Step-by-step solution

If cot⁡x>0⇒1sin⁡x=0\cot x > 0 ⇒ \dfrac{1}{\sin x} = 0 (Not possible)

If cot⁡x<0⇒2cot⁡x+1sin⁡x=0\cot x < 0 ⇒ 2\cot x + \dfrac{1}{\sin x} = 0

⇒2cos⁡x=−1⇒ 2\cos x = - 1

⇒x=2π3⇒ x = \dfrac{2\pi}{3} or 4π3\dfrac{4\pi}{3} (reject as cot⁡x<0\cot x < 0)

So, number of solutions is one.

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