f(x)=sinx+cosx=根号2【sinxcos(π/4)+cosxsin(π/4)】=根号2 sin(x+π/4)
-π/2 ≤ x ≤ π/2
-π/4 ≤ x+π/4 ≤ 3π/4
x∈【-π/4 ,π/2】时单调增
x∈【π/2,3π/4】时单调减
并且sin(-π/4)< sin3π/4
所以最小值=根号2 sin(-π/4)= -1
最大值=根号2 sin(π/2)= 根号2
f(x)=sinx+cosx=根号2【sinxcos(π/4)+cosxsin(π/4)】=根号2 sin(x+π/4)
-π/2 ≤ x ≤ π/2
-π/4 ≤ x+π/4 ≤ 3π/4
x∈【-π/4 ,π/2】时单调增
x∈【π/2,3π/4】时单调减
并且sin(-π/4)< sin3π/4
所以最小值=根号2 sin(-π/4)= -1
最大值=根号2 sin(π/2)= 根号2