Question

已知函数y＝1／2cos²x＋√3／2sinxcosx＋1,x∈R.当函数y取得最大值时,求自变量x的集合

Answer 1

y=1/2*(cos2x+1)/2+√3／2*(2sinxcosx)/2+1

=1/4cos2x+1/4+√3／4*(sin2x)+1

=1/4cos2x+√3／4*sin2x+

=1/2(1/2cos2x++√3／2sin2x)+1

=1/2sin(2x+π/6)+1

当y取最大值时sin(2xπ/6）=1即2x+π/6=π/2加减2kπ,即x=π/6加减kπ

集合是{x|x=π/6加减kπ,k属于Z}