已知0<=x<=π/2,则函数Y=2sinxcos+cos2x的值域是?

问题描述:

已知0<=x<=π/2,则函数Y=2sinxcos+cos2x的值域是?

Y=2sinxcos+cos2x=sin2x+cos2x=根号2sin(2x+π/4),(化间方法根据课本和角公式例题)设2x+π/4=t,则Y=根号2sint因为0<=x<=π/2,所以0<=2x<=π,得π/4<=2x+π/4<=5π/4,即π/4<=t<=5π/4取Y=根号2sin...