函数f(x)=(sin^2x+1/2010sin^2x﹚﹙cos^2x+1/2010cos^2x﹚的最小值是
问题描述:
函数f(x)=(sin^2x+1/2010sin^2x﹚﹙cos^2x+1/2010cos^2x﹚的最小值是
答
f(x)=(sin²x+1/2010sin²x)(cos²x+1/2010cos²x)
=(2011/2010)²sin²xcos²x
=¼(2011/2010)²sin²(2x)
=¼(2011/2010)²[1-cos(4x)]/2
=(2011/2010)²[1-cos(4x)]/8
cos(4x) 取最大值 1 时,f(x) 取得最小值 0