2sin6xcos3x+cos6x<-1

Ответы 1

$2\sin6x\cos3x+\cos6x\ \textless \ -1\\ 4\sin3x\cos^23x + 1-2\sin^23x \ \textless \ -1\\ 4\sin3x(1-\sin^23x) -2\sin^23x\ \textless \ -2\\ 4\sin3x - 4\sin^33x - 2\sin^23x+2\ \textless \ 0\\ 2\sin^33x + \sin^23x - 2\sin3x-1\ \textgreater \ 0 \\\\ u\equiv\sin x\quad u\in[-1;1]\\\\ 2u^3+u^2-2u-1 \ \textgreater \ 0\\ (u^2-1)(2u+1)\ \textgreater \ 0\\ 2u+1\ \textless \ 0,\quad|u|eq1\\ -1\ \textless \ u\ \textless \ -0.5\\ -1\ \textless \ \sin 3x\ \textless \ -0.5\\ -5\pi/6+2\pi k\ \textless \ 3x\ \textless \ -\pi/6+2\pi k,\quad 3xeq-\pi/2+2\pi k\\\\ x\in(-\frac{5\pi}{18}+\frac{2\pi k}{3};-\frac{\pi}{18}+\frac{2\pi k}{3})/\left\{-\frac{\pi}{6}+\frac{2\pi k}{3}ight\},\quad k\in\mathbb{Z}$
- Автор:
  simonin8z
- 5 лет назад
- 0
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