函数y=cos^2+根号3sinxcosx在区间-π/6到π/4的闭区间上的值域是

题目

函数y=cos^2+根号3sinxcosx在区间-π/6到π/4的闭区间上的值域是

答案

y=cos^2 x+根号3sinxcosx
=1/2+1/2 cos2x+√3/2 sin2x
=1/2+sin(2x+π/6)
-π/3≤2x≤π/2
-π/6≤2x+π/6≤2π/3
-1/2≤sin(2x+π/6)≤1
0≤y≤3/2