函数y=sin2分之x减cos2分之x在(负二派,二派]的递增区间是?

y=sin(x/2)-cos(x/2)
=根号2[sin(x/2)cos(π/4)-cos(x/2)sin(π/4)]
=根号2sin[x/2x-π/4)]
-2π≤x≤2π
令t=x/2-π/4,-π-π/4≤t≤π-π/4
当t∈[-π/2,π/2],相当于x∈[-π/2,3π/2]时单调增