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The function $f(x)=\cot x$ is discontinuous on every point of the set
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Verified Answer
The correct answer is:
$\{x=n \pi ; n \in Z\}$
Given, $f(x)=\cot x$
$\Rightarrow \quad f(x)=\frac{\cos x}{\sin x}$
We know that $\sin x=0$, if $f(x)$ is discontinuous
$\therefore$ If $\sin x=0$
$\therefore x=n \pi, n \in n \pi$
So, the given function $f(x)$ is discontinuous on the set $\{x=n \pi, n \in Z\}$
$\Rightarrow \quad f(x)=\frac{\cos x}{\sin x}$
We know that $\sin x=0$, if $f(x)$ is discontinuous
$\therefore$ If $\sin x=0$
$\therefore x=n \pi, n \in n \pi$
So, the given function $f(x)$ is discontinuous on the set $\{x=n \pi, n \in Z\}$
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