Question

giải phương trình sau
sinx+\(\sqrt{3}\) sin\(\frac{x}{2}\) =0

Answer 1

\(\Leftrightarrow2sin\frac{x}{2}cos\frac{x}{2}+\sqrt{3}sin\frac{x}{2}=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}sin\frac{x}{2}=0\\cos\frac{x}{2}=-\frac{\sqrt{3}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\frac{x}{2}=k\pi\\\frac{x}{2}=\pm\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\frac{5\pi}{3}+k4\pi\end{matrix}\right.\)