Question

cos6x-12cos^3x=4-9cosx

Answer 1

$cos6x-12cos^3x=4-9cosx\\cos6x-12cos^3x+9cosx-4=0\\2cos^23x-3cos3x-5=0\\(cos3x+1)(2cos3x-5)=0\\x=\frac{\pi}{3}+\frac{2\pi k}{3}  ,k\in \mathbb{Z}$