Question

find the discontinuities, if any f(x)=(cot x)

Answer 1

cot(x) = 1/tan(x)
So, cot(x) will have discontinuities (because the function will be undefined) when tan(x) = 0.
Do you know when that happens?

Answer 2

what if tanx is undefined also?

Answer 3

\[\cot x = \frac{ \cos x }{ \sin x }\]
So cot x will be discontinuous for all x where sin x = 0.