A$3.$

$($a$)$ Solve cos$((5$x$)/(2))$cos$(($x$)/(2))+$sin$((5$x$)/(2))$sin$(($x$)/(2))=(\backslash$sqrt$(3))/(2)$ for $0<=$x$<2\backslash$pi $.$

$(6$ marks$)$

$($b$)$ The expression $3$x$^(2)-$qx$-7$ leaves a remainder of $2$ when divided

by x$-2.$ Find the value of q$.$