Giải phương trình 1+cosx+cos2x+cos3x=0.

\(1 + \cos x + \cos 2x + \cos 3x = 0\)

\(\left( {1 + \cos 3x} \right) + \left( {\cos x + \cos 2x} \right) = 0\)

\(2\cos \frac{{3x}}{2}\cos \frac{x}{2} + 2{\cos ^2}\frac{{3x}}{2} = 0\)

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

\(4\cos \frac{{3x}}{2}\cos x\cos \frac{x}{2} = 0\)

\[x \in \left\{ {\frac{\pi }{2} + k\pi \,;\,\,\frac{\pi }{3} + \frac{{2k\pi }}{3}} \right\}\].