Question

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

(a) {x : x = nπ, n ∈ Z}

(b) {x : x = 2nπ, n ∈ Z}

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

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

Answer 1

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

Now, f(x) is discontinuous when sinx = 0.

sinx = 0

⇒ x = n$\mathrm{\pi }$, n ∈ Z

So, f(x) = cotx is discontinuous on the set {x : x = nπ, n ∈ Z}

Hence, the correct answer is option (a).