Đáp án:
\(\left[ \matrix{
x = - {\pi \over 4} + k\pi \hfill \cr
x = \pm {{2\pi } \over 3} + k2\pi \hfill \cr} \right.\)
Giải thích các bước giải:
\(\eqalign{
& 1 + \sin x + \cos x + \sin 2x + \cos 2x = 0 \cr
& \Leftrightarrow \sin x + \cos x + 2\sin x\cos x + 2{\cos ^2}x = 0 \cr
& \Leftrightarrow \left( {\sin x + \cos x} \right) + 2\cos x\left( {\sin x + \cos x} \right) = 0 \cr
& \Leftrightarrow \left( {\sin x + \cos x} \right)\left( {1 + 2\cos x} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
\sin x + \cos x = 0 \hfill \cr
1 + 2\cos x = 0 \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
\sin x = - \cos x \hfill \cr
\cos x = - {1 \over 2} \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
\tan x = - 1 \hfill \cr
x = \pm {{2\pi } \over 3} + k2\pi \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
x = - {\pi \over 4} + k\pi \hfill \cr
x = \pm {{2\pi } \over 3} + k2\pi \hfill \cr} \right. \cr} \)
