Question

已知函数f（x ）=(sinx-cosx)sin2x ／sinx (1)求f(x )的定义域及最小正周期 (2)求f(x)的单调增区间

(1)求f(x )的定义域及最小正周期
(2)求f(x)的单调增区间
求详细过程

Answer 1

解答：
（1）sinx≠0， x≠kπ，k∈Z
f(x)=(sinx-cosx)sin2x/sinx
=(sinx-cosx)*2cosx
=2sinxcosx-2cos²x
=sin2x-cos2x-1
=√2sin(2x-π/4)-1
T=2π/2=π
（2）增区间为
2kπ-π/2≤2x-π/4<2kπ或 2kπ<2x-π/4≤2kπ+π/2
2kπ-π/4≤2x<2kπ+π/4或 2kπ+π/4<2x≤2kπ+3π/4
kπ-π/8≤x<kπ+π/8或 kπ+π/8<x≤kπ+3π/8
增区间【 kπ-π/8，kπ+π/8）和（ kπ+π/8，kπ+3π/8】，k∈Z