Căn3 x sinx/2 + cosx/2 = 1

Giải thích các bước giải: \[\begin{array}{l} \sqrt 3 \sin \frac{x}{2} + \cos \frac{x}{2} = 1\\ \Leftrightarrow \frac{{\sqrt 3 }}{2}\sin \frac{x}{2} + \frac{1}{2}\cos \frac{x}{2} = \frac{1}{2}\\ \Leftrightarrow \sin \left( {\frac{x}{2} + \frac{\pi }{6}} \right) = \frac{1}{2}\\ \Leftrightarrow \left[ \begin{array}{l} \frac{x}{2} + \frac{\pi }{6} = \frac{\pi }{6} + k2\pi \\ \frac{x}{2} + \frac{\pi }{6} = \frac{{5\pi }}{6} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = k4\pi \\ x = \frac{{4\pi }}{3} + k4\pi \end{array} \right. \end{array}\]