Question

2sin x + \(\sqrt{2}\) sin 2x = 0

Answer 1

\(\Leftrightarrow2sinx+2\sqrt{2}sinx.cosx=0\)

\(\Leftrightarrow2sinx\left(1+\sqrt{2}cosx\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\cosx=-\frac{\sqrt{2}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\pm\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)