Please complete all the parts with clear steps

$(4\mathrm{.}18$ An LTI system has the impulse response

$h(t)=2\frac{sin(2t)}{t}cos(7t).$

Use the FT to determine the system output if the input is

$($a$)x(t)=cos(2t)+sin(6t)$

$($b$)x(t)={\displaystyle \underset{m=-}{\overset{}{}}}(-1{)}^m(t-m).$

$($c$)x(t)$ as depicted in Fig. P$4\mathrm{.}18($a$).$

$($d$)x(t)$ as depicted in Fig. P$4\mathrm{.}18($b$).$

$($e$)x(t)$ as depicted in Fig. P$4\mathrm{.}18($c$).$

Figure P$4.18$