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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