答：
|x|<=π/4,-π/4<=x<=π/4
f(x)=cos²x+sinx
=1-sin²x+sinx
=-(sinx-1/2)²+1/4
sin(-π/4)<=sinx<=sin(π/4)
-√2/2<=sinx<=√2/2
所以：当sinx-1/2=0即sinx=1/2时f(x)取得最大值1/4