The function f(x) = cot x is discontinuous on the set - Vidyadip

MCQ

The function f(x) = cot x is discontinuous on the set

A
$\{x=2 n \pi: n \in Z \}$
B
$\left\{x=(2 n+1) \frac{\pi}{2} ; n \in Z \right\}$
C
$\left\{x=\frac{n \pi}{2} ; n \in Z \right\}$
✓
$\{x=n \pi: n \in Z \}$

✓

Answer

Correct option: D.

$\{x=n \pi: n \in Z \}$

(d) $\{x=n \pi: n \in Z \}$
Explanation: We have $f ( x )=\cot x$ is continuous in $R-\{n \pi: n \in Z\}$
Since, $f ( x )=\cot x=\frac{\cos x}{\sin x}$ (since, $\sin x =0$ at $n \pi, n \in Z$ )
Hence, $f ( x )=\cot x$ is discontinuous on the set $\{x=n \pi: n \in Z\}$

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