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

Question:

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

(a) $\{x: x=n \pi, n \in Z\}$

(b) $\{x: x=2 m \pi, n \in Z\}$

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

 

(d) $\left\{x: x=\frac{n \pi}{2}, n \in Z\right\}$

Solution:

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

Now, $f(x)$ is discontinuous when $\sin x=0$.

$\sin x=0$

$\Rightarrow x=n \pi, n \in Z$

So, $f(x)=\cot x$ is discontinuous on the set $\{x: x=n \pi, n \in Z\}$

Hence, the correct answer is option (a).

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