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

Trả lời

Lời giải

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

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

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

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

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

\( \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{6} + k2\pi \\3x = \frac{{7\pi }}{6} + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}x = - \frac{\pi }{6} + k2\pi \\x = \frac{{7\pi }}{{18}} + \frac{{k2\pi }}{3}\end{array} \right.\).