求函数y=sin(x+20)-cos(x-10)的值域20.10.是角度

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求函数y=sin(x+20)-cos(x-10)的值域
20.10.是角度

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]