a. Đặt \(t = \cos x\), \(|t| ≤ 1\) ta có:
\(2{t^2} - 3t + 1 = 0 \Leftrightarrow \left[ {\matrix{{t = 1} \cr {t = {1 \over 2}} \cr} } \right. \Leftrightarrow \left[ {\matrix{{\cos x = 1} \cr {\cos x = {1 \over 2}} \cr} } \right. \Leftrightarrow \left[ {\matrix{{x = k2\pi } \cr {x = \pm {\pi \over 3} + k2\pi } \cr} \left( {k \in\mathbb Z} \right)} \right.\)
b. Ta có:
\(\eqalign{& {\cos ^2}x + \sin x + 1 = 0 \Leftrightarrow 1 - {\sin ^2}x + \sin x + 1 = 0 \cr & \Leftrightarrow {\sin ^2}x - \sin x - 2 = 0 \Leftrightarrow \left[ {\matrix{{\sin x = - 1} \cr {\sin x = 2\,\left( {\text {loại }} \right)} \cr} } \right. \Leftrightarrow x = - {\pi \over 2} + k2\pi \cr} \)
c.
\(\sqrt 3 {\tan ^2}x - \left( {1 + \sqrt 3 } \right)\tan x + 1 = 0 \Leftrightarrow \left[ {\matrix{{\tan x = 1} \cr {\tan x = {1 \over {\sqrt 3 }}} \cr} } \right. \Leftrightarrow \left[ {\matrix{{x = {\pi \over 4} + k\pi } \cr {x = {\pi \over 6} + k\pi } \cr} } \right.\left( {k \in\mathbb Z} \right)\)
