MT【51】一道三角求最值问题

【Genius is one percent inspiration and ninety-nine percent perspiration】--- 爱迪生

【Without the one percent of inspiration, all the perspiration in the world is only a bucket of sweat】         ---美国作家Cindi Myers

已知$cosxcos2xcos3x+sinxsin2xsin3x=1$，求$x$=———

解答：记$max\{|cos2x|,|sin2x|\}=t\le1$

$1=cosxcos2xcos3x+sinxsin2xsin3x$

$\le (|cosxcos3x|+|sinxsin3x|)t\le max\{|cos2x|,|cos4x|\}\le |cos2x|\le1$

易知等号要成立:$x=k\pi,k\in Z$

注:$|cos4x|\le |cos2x|$