Phương trình sin 2x = sin (x + pi/3 có nghiệm là

23/38

Phương trình \(\sin 2x = \sin (x + \frac{\pi }{3})\) có nghiệm là

\(\left[ \begin{array}{l}x = \frac{\pi }{3} + k\pi \\x = \frac{\pi }{2} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = \frac{\pi }{6} + \frac{{k\pi }}{3}\\x = \frac{\pi }{3} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = \frac{\pi }{6} + \frac{{k2\pi }}{3}\\x = \frac{\pi }{2} + k2\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

\(\left[ \begin{array}{l}x = \frac{\pi }{3} + k2\pi \\x = \frac{{2\pi }}{9} + \frac{{k2\pi }}{3}\end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

Giải thích

Chọn D

\(\sin 2x = \sin (x + \frac{\pi }{3}) \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{2x = x + \frac{\pi }{3} + k2\pi }\\{2x = \pi - x - \frac{\pi }{3} + k2\pi }\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{3} + k2\pi }\\{x = \frac{{2\pi }}{9} + k\frac{{2\pi }}{3}}\end{array}} \right.\)