y=（tan(x-π/4)）/sinx
tan(x-π/4)中的x-π/4≠π/2+kπ,即x≠3π/4+kπ
sinx≠0,即x≠kπ
综上所述,原方程定义域为
(kπ,3π/4+kπ)∪(3π/4+kπ,(k+1)π),k=0,1,2,3……