Question

giải pt\(\sqrt{3}\)sin3x-cos3x-4sinx.cosx=0

Answer 1

\(\Leftrightarrow\sqrt{3}sin3x-cos3x=2sin2x\)

\(\Leftrightarrow\frac{\sqrt{3}}{2}sin3x-\frac{1}{2}cos3x=sin2x\)

\(\Leftrightarrow sin\left(3x-\frac{\pi}{6}\right)=sin2x\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-\frac{\pi}{6}=2x+k2\pi\\3x-\frac{\pi}{6}=\pi-2x+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{30}+\frac{k2\pi}{5}\end{matrix}\right.\)