Tìm nghiệm phương trình lượng giác cos ( x − 3 π /4 ) + cos ( x + π/ 3 ) = 0 ;

\(\begin{array}{l}{\rm{ }}\cos \left( {x - \frac{{3\pi }}{4}} \right) + \cos \left( {x + \frac{\pi }{3}} \right) = 0 \Leftrightarrow \cos \left( {x - \frac{{3\pi }}{4}} \right) = - \cos \left( {x + \frac{\pi }{3}} \right)\\ \Leftrightarrow \cos \left( {x - \frac{{3\pi }}{4}} \right) = \cos \left( {\pi - \frac{\pi }{3} - x} \right) \Leftrightarrow \cos \left( {x - \frac{{3\pi }}{4}} \right) = \cos \left( {\frac{{2\pi }}{3} - x} \right)\end{array}\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x - \frac{{3\pi }}{4} = \frac{{2\pi }}{3} - x + k2\pi }\\{x - \frac{{3\pi }}{4} = - \frac{{2\pi }}{3} + x + k2\pi }\end{array} \Leftrightarrow \left[ {\begin{array}{*{20}{l}}{2x - \frac{{3\pi }}{4} = \frac{{2\pi }}{3} + k2\pi }\\{0x = \frac{\pi }{{12}} + k2\pi (VL)}\end{array} \Leftrightarrow x = \frac{{17\pi }}{{24}} + k\pi ,k \in \mathbb{Z}} \right.} \right.\)