f(x)=cos²x+sinx=1-sin²x+sinx=-sin²x+sinx+1=-(sinx-1/2)²+5/4
|x|≤π/4
-π/4≤x≤π/4
-√2/2≤sinx≤√2/2
sinx=1/2时,f(x)有最大值f(x)max=5/4
sinx=-√2/2时,f(x)有最小值f(x)min=(1-√2)/2
函数的值域为[(1-√2)/2,5/4]