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

\begin{array}{1 1}(A)\;\left \{x=n\pi:n\in z\right \} & (B)\;\left \{x=2n\pi:n\in z\right \}\\(C)\;\left \{x=(2n+1)\frac{\pi}{2};n\in z\right \} & (D)\;\left \{x=\frac{n\pi}{2};n\in z\right \}\end{array}

Toolbox:
• The general solution for $x$ in $\cot x$ is $x=n\pi+\alpha$
• A function is said to be differentiable at every point in its domain.
$f(x)=\cot x$
The general solution is $\theta=n\pi+\alpha,n\in z$
Hence the function is discontinuous on the set $\left\{x=n\pi,n\in z\right\}$
The correct option is $A$.