Given the electric field of a complete amplitude modulated wave as $$$\vec{E} = \hat{i}E_c\left(1 + \frac{E_m}{E_c}\cos\omega_m t\right)\cos\omega_c t$$$ Where the subscript c stands for the carrier wave and m for the modulating signal. The frequencies present in the modulated wave are

A

$$\omega_c$$ and $$\sqrt{\omega_c^2 + \omega_m^2}$$

B

$$\omega_c, \omega_c + \omega_m$$ and $$\omega_c - \omega_m$$

C

$$\omega_c$$ and $$\omega_m$$

D

$$\omega_c$$ and $$\sqrt{\omega_c \omega_m}$$