函数f(x)=sin(x+π/6)+cos(x+π/6)的值域为

题目

函数f(x)=sin(x+π/6)+cos(x+π/6)的值域为

答案

f(x)=sin(x+π/6)+cos(x+π/6)
=根号2[ sin(x+π/6)cos(π/4)+cos(x+π/6)sin(π/4) ]
=根号2 sin(x+π/6+π/4)
值域：【-根号2,根号2】