Question

2sin6xcos3x+cos6x<-1

Answer 1

$2sin6xcos3x+cos6x textless -1\ 4sin3xcos^23x + 1-2sin^23x textless -1\ 4sin3x(1-sin^23x) -2sin^23x textless -2\ 4sin3x - 4sin^33x - 2sin^23x+2 textless 0\ 2sin^33x + sin^23x - 2sin3x-1 textgreater 0 \\ uequivsin xquad uin[-1;1]\\ 2u^3+u^2-2u-1 textgreater 0\ (u^2-1)(2u+1) textgreater 0\ 2u+1 textless 0,quad|u|neq1\ -1 textless u textless -0.5\ -1 textless sin 3x textless -0.5\ -5pi/6+2pi k textless 3x textless -pi/6+2pi k,quad 3xneq-pi/2+2pi k\\ xin(-frac{5pi}{18}+frac{2pi k}{3};-frac{pi}{18}+frac{2pi k}{3})/left{-frac{pi}{6}+frac{2pi k}{3}right},quad kinmathbb{Z}$