已知函数f(x)等于2cosx(sinx-cosx)+1,X属于R 求函数的单调递增区间

f(x)=2cosx(sinx-cosx)+1
=2cosxsinx-2cos²x+1
=sin2x-cos2x
=√2sin(2x-π/4)
-π/2+2kπ<2x-π/4<π/2+2kπ
-π/4+2kπ<2x<3π/4+2kπ
-π/8+kπx∈[-π/8+kπ,3π/8+kπ]k∈z
望采纳~~~~~~~