$$\eqalign{
& a)\,\,\cos \left( {3x + {{10}^0}} \right) = - 1 \cr
& \Leftrightarrow 3x + {10^0} = {180^0} + k{360^0} \cr
& \Leftrightarrow 3x = {170^0} + k{360^0} \cr
& \Leftrightarrow x = {{{{170}^0}} \over 3} + k{120^0}\,\,\left( {k \in Z} \right) \cr
& b)\,\,\,\sin 2x - \cos x = 0 \cr
& \Leftrightarrow 2\sin x\cos x - \cos x = 0 \cr
& \Leftrightarrow \cos x\left( {2\sin x - 1} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
\cos x = 0 \hfill \cr
\sin x = {1 \over 2} \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = {\pi \over 2} + k\pi \hfill \cr
x = {\pi \over 6} + k2\pi \hfill \cr
x = {{5\pi } \over 6} + k2\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr
& c)\,\,\,\tan x - \tan 2x = - 1 \cr
& \Leftrightarrow {{\sin x} \over {\cos x}} - {{\sin 2x} \over {\cos 2x}} = - 1 \cr
& \Leftrightarrow \sin x\cos 2x - \sin 2x\cos x = - \cos x\cos 2x \cr
& \Leftrightarrow \sin \left( {x - 2x} \right) = - \cos x\cos 2x \cr
& \Leftrightarrow - \sin x = - \cos x\cos 2x \cr
& \Leftrightarrow \sin x = \cos x\left( {2{{\cos }^2}x - 1} \right) \cr
& \Leftrightarrow \sin x = 2{\cos ^3}x - \cos x \cr
& \Leftrightarrow 2{\cos ^3}x - \sin x - \cos x = 0 \cr
& TH1:\,\,\cos x = 0 \Rightarrow \sin x = \pm 1 \cr
& \Rightarrow Vo\,\,nghiem \cr
& TH2:\,\,\cos x \ne 0 \cr
& \Leftrightarrow 2 - \tan x\left( {1 + {{\tan }^2}x} \right) - \left( {1 + {{\tan }^2}x} \right) = 0 \cr
& \Leftrightarrow 2 - \tan x - {\tan ^3}x - 1 - {\tan ^2}x = 0 \cr
& \Leftrightarrow {\tan ^3}x + {\tan ^2}x + \tan x - 1 = 0 \cr
& .. \cr} $$
