已知函数f(x)=［1-根号2sin(2x-π/4）］/cosx 1）求F(X)的定义域 2）

f(x) = {1-√2sin(2x-π/4)}/cosx
= {1-(√2sin2xcosπ/4-cos2xsinπ/4)}/cosx
= {1-(sin2x-cos2x)}/cosx
= {1-sin2x+cos2x}/cosx
= {1-2sinxcosx+2cos^2x-1}/cosx
= {-2sinxcosx+2cos^2x}/cosx
= 2(cosx-sinx)
要使函数有意义,则必须要求sin(2x-π/4)≥0且cosx≠0,
所以要求2kπ≤2x-π/4≤2kπ+π,(k∈Z)且x≠kπ +π/2,(k∈Z)
即kπ+π/8≤x≤kπ+5π/8且x≠kπ +π/2,(k∈Z),所以f(x)的定义域为 [kπ+π/8,kπ +π/2)∪(kπ +π/2,kπ+5π/8] (k∈Z)