f(x)=2cosx(sinx-cosx)+1
=2sinxcosx-2(cosx)^2+1
=sin2x-cos2x-1+1
=√2(√2/2*sin2x-√2/2*cos2x)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
∵x∈[π/8,3π/4],得 0
f(x)=2cosx(sinx-cosx)+1
=2sinxcosx-2(cosx)^2+1
=sin2x-cos2x-1+1
=√2(√2/2*sin2x-√2/2*cos2x)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
∵x∈[π/8,3π/4],得 0