【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:$|cos4x|\le |cos2x|$