y=cos(2x-1/2)-cos(x-1/4)的值域是?

y=cos(2x-1/2)-cos(x-1/4)的值域是?
y=cos(2x-1/2)-cos(x-1/4)的值域是?

y=cos(2x-1/2)-cos(x-1/4)的值域是?
y=cos(2x-1/2)-cos(x-1/4)=cos2(x-1/4)-cos(x-1/4)=2[cos(x-1/4)]^2-cos(x-1/4)-1
令cos(x-1/4)=n则原式为
2n^2-n-1=2(n-1/4)^2-9/8
-1≤n≤1 -5/4≤n-1/4≤3/4 0≤ (n-1/4)^2≤25/16 0 ≤2(n-1/4)^2≤25/8 -9/8≤2(n-1/4)^2-9/8≤2
所以原式的值域为【-9/8,2】