函数y=1/2(sinx+cosx)-1/2[sinx-cosx],求他的值域.[ ]代表绝对值

sinx-cosx=√2sin(x-π/4)令sin(x-π/4)≥0解得:2kπ+π/4≤x≤(2k+1)π+π/4所以当2kπ+π/4≤x≤(2k+1)π+π/4时sinx-cosx≥0当(2k+1)π+π/4≤x≤(2k+2)π+π/4时sinx-cosx≤0所以当2kπ+π/4≤x≤(2k+1)π+π/4...