b, \(cosx+cos2x+cos3x+cos4x=0\)
\(\Leftrightarrow2cos\dfrac{5x}{2}.cos\dfrac{3x}{2}+2cos\dfrac{5x}{2}.cos\dfrac{x}{2}=0\)
\(\Leftrightarrow2cos\dfrac{5x}{2}\left(cos\dfrac{3x}{2}+cos\dfrac{x}{2}\right)=0\)
\(\Leftrightarrow4cos\dfrac{5x}{2}.cosx.cos\dfrac{x}{2}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos\dfrac{5x}{2}=0\\cosx=0\\cos\dfrac{x}{2}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5x}{2}=\dfrac{\pi}{2}+k2\pi\\x=\dfrac{\pi}{2}+k2\pi\\\dfrac{x}{2}=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{5}+\dfrac{k4\pi}{5}\\x=\dfrac{\pi}{2}+k2\pi\\x=\pi+k4\pi\end{matrix}\right.\)
