f(x)=cos^4x-2sinxcosx-sin^4x
=cos2x-sin2x
=√2cos(2x+π/4)
最小正周期为2π/2=π
x∈[0,π/2]
2x+π/4∈[π/4,3π/4]
所以
cos(2x+π/4)∈[-√2/2,√2/2]
所以
f(x)的最小值为 -1
2x+π/4=3π/4
得 x=π/4