Question

At which values is \[\tan x=\dfrac{\sin x}{\cos x}\] not continuous?

Options

• \[x=2n\pi,\ n\in\mathbb{Z}\]

• \[x=\dfrac{(2n+1)\pi}{2},\ n\in\mathbb{Z}\]

• \[x=n\pi,\ n\in\mathbb{Z}\]

• \[x=\dfrac{n\pi}{2},\ n\in\mathbb{Z}\]

Answer 1

The function \[\tan x\] is continuous wherever \[\cos x\neq 0\]. Since \[\cos x=0\] at \[x=\frac{(2n+1)\pi}{2}\], \[\tan x\] is not continuous at those values.