Question

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

• A. \(\left\{x=(2n+1)\frac{\pi}{2};n∈ Z\right\}\)
• B. \(\left\{x=n\pi;\ n∈Z\right\}\)
• C. \(\left\{x=\frac{n\pi}{2};\ n∈Z\right\}\)
• D. \(\left\{{x=2n\pi;\ n ∈Z}\right\}\)

Hint:

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.

Answer 1

The Correct Option is B

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

Answer 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) \( \left\{ x = n\pi ;\ n \in \mathbb{Z} \right\} \).