Đáp án:
$$\left[ \matrix{
x = {{5\pi } \over {36}} + {{k2\pi } \over 3} \hfill \cr
x = - {{11\pi } \over {12}} + k2\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right)$$
Giải thích các bước giải:
$$\eqalign{
& \cos \left( {2x + {\pi \over 4}} \right) + \cos \left( {x + {\pi \over 3}} \right) = 0 \cr
& \Leftrightarrow \cos \left( {2x + {\pi \over 4}} \right) = - \cos \left( {x + {\pi \over 3}} \right) \cr
& \Leftrightarrow \cos \left( {2x + {\pi \over 4}} \right) = \cos \left( {\pi - x - {\pi \over 3}} \right) \cr
& \Leftrightarrow \cos \left( {2x + {\pi \over 4}} \right) = \cos \left( {{{2\pi } \over 3} - x} \right) \cr
& \Leftrightarrow \left[ \matrix{
2x + {\pi \over 4} = {{2\pi } \over 3} - x + k2\pi \hfill \cr
2x + {\pi \over 4} = - {{2\pi } \over 3} + x + k2\pi \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
x = {{5\pi } \over {36}} + {{k2\pi } \over 3} \hfill \cr
x = - {{11\pi } \over {12}} + k2\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr} $$
