A sinusoidal signal is represented as $$x(t) = \mathrm{cos}(\omega t) = \mathrm{cos}(2\pi f t)$$

$w$ is angular frequency and $f$ is frequency. See Frequency definition

Your signal $x(t) = 5 + 30\mathrm{cos}(2000\pi t) + 10\mathrm{cos}(6000\pi t) = 5\mathrm{cos}(2\pi \times 0 t) + 30\mathrm{cos}(2\pi \times 1000 t) + 10\mathrm{cos}(2\pi \times 3000 t)$

There are three frequencies $0, 1000, \textrm{ and } 3000\textrm{Hz}$ thus the bandwidth is $3000\textrm{Hz}$.

A sinusoidal signal is represented as $$x(t) = \mathrm{cos}(\omega t) = \mathrm{cos}(2\pi f t)$$

$\omega$ is the angular frequency and $f$ is the frequency. See Frequency definition.

Your signal \begin{align} x(t) &= 5 + 30\mathrm{cos}(2000\pi t) + 10\mathrm{cos}(6000\pi t)\\ &= 5\mathrm{cos}(2\pi \times 0 t) + 30\mathrm{cos}(2\pi \times 1000 t) + 10\mathrm{cos}(2\pi \times 3000 t)\end{align}

There are three frequencies $0, 1000, \textrm{ and } 3000\textrm{Hz}$ thus the bandwidth is $3000\textrm{Hz}$.