f(x)=[1-√2sin(2x-π/4)]/cosx
∵cosx≠0 ∴该函数的定义域为：x≠kπ+π/2
当cosx≠0 时,
f(x)=(1-sin2x+cos2x)/cosx=2(cosx-sinx)=2√2sin(π/4-x)
∴该函数的最小正周期是T=2π,
单调增区间是：[2kπ+3π/4,kπ+3π/2）∪（kπ+3π/2,2kπ+7π/4]