Giải phương trình sin 2x + cos ( 6x + pi /3) = 0

Trả lời

Lời giải

\(\sin 2x + \cos \left( {6x + \frac{\pi }{3}} \right) = 0\)

\( \Leftrightarrow \cos \left( {6x + \frac{\pi }{3}} \right) = - \sin 2x\)

\[ \Leftrightarrow \cos \left( {6x + \frac{\pi }{3}} \right) = \cos \left( {2x + \frac{\pi }{2}} \right)\]

\( \Leftrightarrow \left[ \begin{array}{l}6x + \frac{\pi }{3} = 2x + \frac{\pi }{2} + k2\pi \\6x + \frac{\pi }{3} = - 2x - \frac{\pi }{2} + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}4x = \frac{\pi }{6} + k2\pi \\8x = - \frac{{5\pi }}{6} + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{24}} + k\frac{\pi }{2}\\x = - \frac{{5\pi }}{{48}} + k\frac{\pi }{4}\end{array} \right.\).