$4\mathrm{.}7-3$ Let s$($t$)$ be an angle$-$modulated signal that arrives at a receiver,

s$($t$)=2$cos$(10^7*$pi$*$t $+2*$sin$(1000$pit $+0\mathrm{.}3$pi$)-3$pi cos$(2000$t$))$

$($a$)$ Find the bandwidth of this FM signal

$($b$)$ If s$($t$)$ is sent to an $($ideal$)$ envelope detector, find the detector output signal