$\begin{array}{l}a)\,\,2\cos^2x-\sin^2x-4\cos x+2=0\\ \Leftrightarrow 2\cos^2x - (1 - \cos^2x) - 4\cos x + 2 = 0\\ \Leftrightarrow 3\cos^2x - 4\cos x + 1 = 0\\ \Leftrightarrow \left[\begin{array}{l}\cos x = 1\\\cos x = \dfrac{1}{3}\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = k2\pi\\x = \pm \arccos\dfrac{1}{3} + k2\pi\end{array}\right.\quad (k \in \Bbb Z)\\ b)\,\,\sin^2x-2\cos x+2=0\\ \Leftrightarrow 1 - \cos^2x - 2\cos x + 2 = 0\\ \Leftrightarrow \cos^2x + 2\cos x - 3 = 0\\ \Leftrightarrow \left[\begin{array}{l}\cos x = 1\\\cos x = -3\quad (loại)\end{array}\right.\\ \Leftrightarrow x = k2\pi \quad (k \in \Bbb Z) \end{array}$
