Modulated signal,
$$
\begin{aligned}
\phi_{\mathrm{AM}}(t) & =A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t \\
& =A_{c}\left[1+\frac{2}{A_{c}} \cos \omega_{m} t\right] \cos \omega_{c} t \\
\mu & =\frac{2}{A_{c}}
\end{aligned}
$$
Condition for envelope detection of an AM signal is,
$$
\begin{aligned}
\mu & \leq 1 \\
\Rightarrow \quad \frac{2}{A_{c}} & \leq 1 \text { or } A_{c} \geq 2
\end{aligned}
$$
Therefore minimum value of $A_{c}$ should be 2 .
