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

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

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