a,
$\sqrt3\sin x-\cos x=m-1$ có nghiệm
$\to 3+1\ge (m-1)^2$
$\to |m-1|\le 2$
$\to -2\le m-1\le 2$
$\to -1\le m\le 3$
b,
$m\sin2x+(2m-1)\cos2x=3m+2$ có nghiệm
$\to m^2+(2m-1)^2\ge (3m+2)^2$
$\to m^2+4m^2-4m+1\ge 9m^2+12m+4$
$\to 4m^2+16m+3\le 0$
$\to \dfrac{-4-\sqrt{13}}{2}\le m\le \dfrac{-4+\sqrt{13}}{2}$