已知函数f（x）=2cosx(sinx-cosx)+1,x属于R.（1）求函数f(x)的最小正周期;(2)求函数f(x)

f(x)=2cosx(sinx-cosx)+1
=2sinxcosx-2(cosx)^2+1
=2sinxcosx-[2(cosx)^2-1]
=sin2x-cos2x
=√2(√2/2*sin2x-√2/2*cos2x)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
（1）
f(x)=√2sin(2x-π/4)
∴函数f(x)的最小正周期:
T=2π/2=π
（2）f(x)=2sinxcosx+1-2cosx^2
=sin2x-cos2x
=√2sin(2x-π/4)
π/8≤x≤3π/4
得 0≤2x-π/4≤5π/4
f(x）最小值是＝√2sin5π/4=-1
f(x）最大值是＝√2 2sinπ/2=√2