Question

\(4sin\left(2x+\frac{3\pi}{5}\right)c\text{os}\left(2x+\frac{3\pi}{5}\right)-\sqrt{3}=0\)

Answer 1

\(\Leftrightarrow2sin\left(4x+\frac{6\pi}{5}\right)=\sqrt{3}\)

\(\Leftrightarrow sin\left(4x+\frac{6\pi}{5}\right)=\frac{\sqrt{3}}{2}\)

\(\Rightarrow\left[{}\begin{matrix}4x+\frac{6\pi}{5}=\frac{\pi}{3}+k2\pi\\4x+\frac{6\pi}{5}=\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-\frac{13\pi}{60}+\frac{k\pi}{2}\\x=-\frac{2\pi}{15}+\frac{k\pi}{2}\end{matrix}\right.\)