Question

y=cos(2x-1/2派）－cos(x-1/4派)（x属于［0,派］）的值域是

Answer 1

y=cos(2x-π/2)-cos(x-π/4)=cos2(x-π/4)-cos(x-π/4)=2[cos(x-π/4)]^2-cos(x-π/4)-1

令cos(x-π/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】