1) $sin2x+3m^2-m-1=0$
$↔ 3m^2-m-1=-sin2x$
Vì $sin2x∈[-1;1]$ nên $-1≤3m^2-m-1≤1$
$↔ -\dfrac{2}{3}≤m≤0$ hoặc $\dfrac{1}{3}≤m≤1$
2) $cos^2x+2sinx+m-3=0$
$↔ 1-sin^2x+2sinx+m-3=0$
$↔ -(sin^2x-2sinx+1)+m-1=0$
$↔ m-1=(sinx-1)^2$
Vì $sinx∈[-1;1]$ nên $sinx-1∈[-2;0] → (sinx-1)^2∈[0;4]$
$→ 0≤m-1≤4$
$↔ 1≤m≤5$