(1)保证tanx及tan(x/2)有意义,有x≠kπ+π/2,x/2≠kπ+π/2,联立解得x≠kπ+π/2且x≠2kπ+π (k∈Z)
(2)y=sin2xtanx+sinxtan(x/2)
=2sinxcosxsinx/cosx+sinx[(1-cos)/sinx]
=2sin²x+1-cos
=2(1-cos²x)+1-cosx
= -2cos²x-cosx+3
=(25/8)-2(cosx+1/4)²
当cosx=1时,y取得最小值0
当cosx= -1时,y取得最大值2
(3)见上面