Question

Giải phương trình \(\sin 2x = \sin \left( {x + \frac{\pi }{4}} \right)\)

Answer 1

\(\sin 2x = \sin \left( {x + \frac{\pi }{4}} \right) \Leftrightarrow \left[ \begin{array}{l}2x = x + \frac{\pi }{4} + k2\pi \\2x = \pi  - \left( {x + \frac{\pi }{4}} \right) + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\3x = \frac{{3\pi }}{4} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = \frac{\pi }{4} + \frac{{k2\pi }}{3}\end{array} \right.\)