Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
22,\\
4{\cos ^3}x - \cos 2x - 4\cos x + 1 = 0\\
 \Leftrightarrow 4{\cos ^3}x - \left( {2{{\cos }^2}x - 1} \right) - 4\cos x + 1 = 0\\
 \Leftrightarrow 4{\cos ^3}x - 2{\cos ^2}x + 1 - 4\cos x + 1 = 0\\
 \Leftrightarrow 4{\cos ^3}x - 2{\cos ^2}x - 4\cos x + 2 = 0\\
 \Leftrightarrow 2{\cos ^3}x - {\cos ^2}x - 2\cos x + 1 = 0\\
 \Leftrightarrow {\cos ^2}x\left( {2\cos x - 1} \right) - \left( {2\cos x - 1} \right) = 0\\
 \Leftrightarrow \left( {2\cos x - 1} \right)\left( {{{\cos }^2}x - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\cos x = \dfrac{1}{2}\\
{\cos ^2}x = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
\cos x = \dfrac{1}{2}\\
{\sin ^2}x = 0
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x =  \pm \dfrac{\pi }{3} + k2\pi \\
x = k\pi 
\end{array} \right.\\
23,\\
{\cos ^2}3x.\cos 2x - {\cos ^2}x = 0\\
 \Leftrightarrow \left( {4{{\cos }^3}x - 3\cos x} \right).\left( {2{{\cos }^2}x - 1} \right) - {\cos ^2}x = 0\\
 \Leftrightarrow 8{\cos ^5}x - 4{\cos ^3}x - 6{\cos ^3}x + 3\cos x - {\cos ^2}x = 0\\
 \Leftrightarrow 8{\cos ^5}x - 10{\cos ^3}x - {\cos ^2}x + 3\cos x = 0\\
 \Leftrightarrow \cos x.\left( {8{{\cos }^4}x - 10{{\cos }^2}x - \cos x + 3} \right) = 0\\
 \Leftrightarrow \cos x.\left[ {\left( {8{{\cos }^4}x - 8{{\cos }^3}x} \right) + \left( {8{{\cos }^3}x - 8{{\cos }^2}x} \right) - \left( {2{{\cos }^2}x - 2\cos x} \right) - \left( {3\cos x - 3} \right)} \right] = 0\\
 \Leftrightarrow \cos x\left( {\cos x - 1} \right)\left( {8{{\cos }^3}x + 8{{\cos }^2}x - 2\cos x - 3} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
\cos x = 1\\
\cos x = 0,574....
\end{array} \right.
\end{array}\)