y=sin(x+20)-cos(x-10)
=sin(x+20)-sin[90-(x-10)]
=sin(x+20)-sin(100-x)
=sin(x+20)-sin[180-(100-x)]
=sin(x+20)-sin(x+80)
和差化积
=2cos(x+50)*sin(-30)
=-cos(x+50)
所以值域[-1,1]