Question:

The function f(x) = cot x is discontiuous on every point of the set

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For trigonometric functions like $ \cot(x) $, look for values where the denominator of the function becomes zero. For $ \cot(x) = \frac{\cos(x)}{\sin(x)} $, the function is undefined whenever $ \sin(x) = 0 $, which happens at multiples of $ \pi $. These are the points of discontinuity.

Updated On: Mar 29, 2025

$\left\{x=(2n+1)\frac{\pi}{2};n∈ Z\right\}$
$\left\{x=n\pi;\ n∈Z\right\}$
$\left\{x=\frac{n\pi}{2};\ n∈Z\right\}$
$\left\{{x=2n\pi;\ n ∈Z}\right\}$

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The Correct Option is B

Approach Solution - 1

The correct answer is (B) : $\left\{x=n\pi;\ n∈Z\right\}$.

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Approach Solution -2

The correct answer is: (B) $ \left\{ x = n\pi ;\ n \in \mathbb{Z} \right\} $.

The function $ f(x) = \cot(x) $ is discontinuous at points where the denominator of the cotangent function is zero. The cotangent function is defined as:

$ \cot(x) = \frac{\cos(x)}{\sin(x)} $

The function $ \cot(x) $ is undefined when $ \sin(x) = 0 $, which occurs at multiples of $ \pi $, i.e., $ x = n\pi $, where $ n \in \mathbb{Z} $ (the set of all integers). Therefore, $ f(x) = \cot(x) $ is discontinuous at $ x = n\pi $, for $ n \in \mathbb{Z} $. Thus, the correct answer is (B) $ \left\{ x = n\pi ;\ n \in \mathbb{Z} \right\} $.