Cos(3x-π/6)+cos(x+π/4)=0

[latex]cosa+cosb=2cos\frac{a+b}{2}cos\frac{a-b}{2}\\\\cos(3x-\frac{\pi}{6})+cos(x+\frac{\pi}{4})=0\\2cos(2x-\frac{\pi}{6})cos(x-\frac{5\pi}{6})=0\\\\1)cos(2x-\frac{\pi}{6})=0\\2x-\frac{\pi}{6}=\frac{\pi}{2}+\pi n\\2x=\frac{2\pi}{3}+\pi n\\x=\frac{\pi}{3}+\frac{\pi n}{2}, \; n\in Z;\\\\2)cos(x-\frac{5\pi}{6})=0\\x-\frac{5\pi}{6}=\frac{\pi}{2}+\pi k\\x=\frac{4\pi }{3}+\pi k, \; k\in Z.[/latex]