已知函数f(x)=cos^2(x/2)-sin(x/2)*cos(x/2)-1/2

f(x)=cos²(x/2)-sin(x/2)*cos(x/2)-1/2
=1/2*[2cos²(x/2)-1]-1/2*sinx
=1/2*cosx-1/2*sinx
=√2/2*(√2/2*cosx-√2/2*sinx)
=√2/2*cos(x+π/4)
最小正周期为：T=2π/1=2π
∵-1≤cos(x+π/4)≤1
∴-√2/2≤f(x)≤√2/2
即值域为[-√2/2,√2/2]
∵f(α)=√2/2*cos(x+π/4)
=3√2/2
∴cos(x+π/4)=3 >1,不可能成立的!

f(x)=cos^2(x/2)-sin(x/2)*cos(x/2)-1/2
=1/2(cosx-sinx)
=√2/2cos(x+π/4)
最小正周期：[-π/4,7π/4]
值域：[-√2/2,√2/2]
√2/2cos(x+π/4)=3√2/2
cos(x+π/4)=3(不成立)