Question

已知y=1/2cos^x+根号3/2sinxcosx+1.x属于R.函数取得最大值向量x的集合

Answer 1

y=1/2cos^x+√3/2sinxcosx+1=(1+cos2x)/4+√3/4sin2x+1

=(√3/4sin2x+1/4cos2x)+5/4

=1/2sin(2x+π/6)+5/4

取最大值则sin(2x+π/6)=1

所以2x+π/6=2kπ+π/2

2x=2kπ+π/3

x=kπ+π/6

X={x|x=kπ+π/6 k属于整数}