1) $\cos4x - 3\sqrt2\cos2x + 3\sqrt2 - 1= 0$
$\Leftrightarrow 2\cos^22x - 1 -3\sqrt2\cos2x + 3\sqrt2 - 1= 0$
$\Leftrightarrow 2\cos^22x -3\sqrt2\cos2x + 3\sqrt2 - 2= 0$
$\Leftrightarrow \left[\begin{array}{l}\cos2x = 1\\\cos2x =\dfrac{3\sqrt2 - 2}{2}\quad (loại)\end{array}\right.$
$\Leftrightarrow 2x = k2\pi$
$\Leftrightarrow x = k\pi\quad (k\in\Bbb Z)$
2) $\sin x + (m-1)\cos x = \sqrt5$
Phương trình có nghiệm $\Leftrightarrow 1^2 + (m-1)^2 \geq (\sqrt5)^2$
$\Leftrightarrow (m -1)^2 \geq 4$
$\Leftrightarrow \left[\begin{array}{l}m \geq 3\\m \leq -1\end{array}\right.$
