`a) 3cos² x + 2cos x - 1 = 0`
`<=>` \(\left[ \begin{array}{l}cos x = \dfrac{1}{3}\\cos x = -1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = ±arccos \dfrac{1}{3} + k2π\\x = π + k2π\end{array} \right.\) `(k ∈ ZZ)`
`b) 2sin² x + 5cos x + 1 = 0`
`<=> 2 - 2cos² x + 5cos x + 1 = 0`
`<=> -2cos² x + 5cos x + 3 = 0`
`<=>` \(\left[ \begin{array}{l}cos x = 3 (l)\\cos x = -\dfrac{1}{2}\end{array} \right.\)
`<=> x = ±(2π)/3 + k2π`
`c) cos² x - 4cos x + 5/2 = 0`
`<=> 2cos² x - 8cos x + 5 = 0`
`<=>` \(\left[ \begin{array}{l}cos x = \dfrac{4 + \sqrt{6}}{2} (l)\\x = \dfrac{4 - \sqrt{6}}{2}\end{array} \right.\)
`<=> x = ±arccos ((4 - \sqrt{6})/2) + k2π` `(k ∈ ZZ)`
`d) cos² x - cos x - 2 = 0`
`<=>` \(\left[ \begin{array}{l}cos x = 2 (l)\\cos x = -1\end{array} \right.\)
`<=> x = π + k2π` `(k ∈ ZZ)`
`e) 16 - 15sin² x - 8cos x = 0`
`<=> 16 - 15 + 15cos² x - 8cos x = 0`
`<=> 15cos² x - 8cos x + 1 = 0`
`<=>` \(\left[ \begin{array}{l}cos x = \dfrac{1}{3}\\cos x = \dfrac{1}{5}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = ±arccos \dfrac{1}{3} + k2π\\x = arccos \dfrac{1}{5} + k2π\end{array} \right.\) `(k ∈ ZZ)`
