P$1.$ Consider the modulated signal expressed as below where $cos(2000t)$ represents the carrier, $s(t)=20[cos(300t)cos(2000t)+sin(300t)sin(2000t)]$

$($a$)$ Find the complex envelope for the modulated signal.

$($b$)$ Find the quadrature modulation components $x(t)$ and $y(t)$ for this modulated signal.

$($c$)$ Find the amplitude and phase modulation components $R(t)$ and $(t).$

$($d$)$ Find the normalized average power of $s(t).$

$($e$)$ What is the type of modulation