QJEEM21Mae1c2: JEE Main 2021 Mathematics - Class 11 JEEM21Mae1c2 Solution: The number of solutions of the equation

Question

Verified Solution • 2025–26 Session moderate

The number of solutions of the equation

| \cot x | = \cot x + \frac{1}{\sin x}

in the interval [ 0, 2

π

] is

Accepted Answer

Case I : When cot x > 0,

x \in [0, \frac{π}{2}] \cup [π, \frac{3 π}{2}]

\cot x = \cot x + \frac{1}{\sin x} \Rightarrow

not possible

Case II : When cot x < 0,

x \in [\frac{π}{2}, π] \cup [\frac{3 π}{2}, 2 π]

- \cot x = \cot x + \frac{1}{\sin x}

\Rightarrow \frac{- 2 \cos x}{\sin x} = \frac{1}{\sin x}

\Rightarrow \cos x = \frac{- 1}{2}

\Rightarrow x = \frac{2 π}{3}, \frac{4 π}{3}

(Rejected)

One solution.

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