a.
\(\eqalign{
& 2\cos x - \sqrt 3 = 0 \Leftrightarrow \cos x = {{\sqrt 3 } \over 2} \Leftrightarrow \cos x = \cos {\pi \over 6} \cr
& \Leftrightarrow x = \pm {\pi \over 6} + k2\pi ,k \in\mathbb Z \cr} \)
b.
\(\eqalign{
& \sqrt 3 \tan 3x - 3 = 0 \Leftrightarrow \tan 3x = \sqrt 3 \Leftrightarrow \tan 3x = \tan {\pi \over 3} \cr
& \Leftrightarrow 3x = {\pi \over 3} + k\pi \Leftrightarrow x = {\pi \over 9} + k{\pi \over 3};k \in\mathbb Z \cr} \)
c.
\(\eqalign{& \left( {\sin x + 1} \right)\left( {2\cos 2x - \sqrt 2 } \right) = 0 \cr & \Leftrightarrow \left[ {\matrix{{\sin x + 1 = 0} \cr {2\cos 2x - \sqrt 2 = 0} \cr} } \right. \Leftrightarrow \left[ {\matrix{{\sin x = - 1} \cr {\cos 2x = {{\sqrt 2 } \over 2}} \cr} } \right. \cr & \Leftrightarrow \left[ {\matrix{{x = - {\pi \over 2} + k2\pi } \cr {2x = \pm {\pi \over 4} + k2\pi } \cr} } \right. \Leftrightarrow \left[ {\matrix{{x = - {\pi \over 2} + k2\pi } \cr {2x = \pm {\pi \over 8} + k\pi } \cr} } \right. \cr} \)
