函数f(x)=sinx-tanx,x属于[-π/4,π/4] 求值域

答案写错了吧!
f(x) = sinx – tanx
求导：f ′(x) = cosx - 1/cos²x = (cos³x-1)/cos²≤0,定义域上单调减
在区间【-π/4,π/4】
最小值f(π/4) = sinπ/4 - tanπ/4 = √2/2 - 1
最大值f(-π/4) = sin(-π/4) - tan(-π/4) = -√2/2 + 1