## Calculus (3rd Edition)

The function $\tan 2t$ is discontinuous at $$t=\frac{(2n+1)\pi}{4}$$ and the discontinuity is infinite.
Since $\tan 2t=\frac{\sin 2t }{\cos 2t}$, then the function is discontinuous when $$\cos 2t =0.$$ That is, $2t=\frac{(2n+1)\pi}{2}$, n is integer. This means that the function $\tan 2t$ is discontinuous at $$t=\frac{(2n+1)\pi}{4}$$ and the discontinuity is infinite.