Question

giải pt \(cos\left(2x+\frac{2\pi}{3}\right)+3cos\left(x+\frac{\pi}{3}\right)+2=0\)

Answer 1

\(\Leftrightarrow2cos^2\left(x+\frac{\pi}{3}\right)-1+3cos\left(x+\frac{\pi}{3}\right)+2=0\)

\(\Leftrightarrow2cos^2\left(x+\frac{\pi}{3}\right)+3cos\left(x+\frac{\pi}{3}\right)+1=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos\left(x+\frac{\pi}{3}\right)=-1\\cos\left(x+\frac{\pi}{3}\right)=-\frac{1}{2}\end{matrix}\right.\)

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

\(\Leftrightarrow...\)