若x>0,y>0,0
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若x>0,y>0,0 C.恒等于零
D.符号随xy的取值而定
D.符号随xy的取值而定
f(x)=sin(x+y)-[sinx+siny]=2sin[(x+y)/2]cos[(x+y)/2]-2sin[(x+y)/2]cos[(x-y)/2]=2sin[(x+y)/2]{cos[(x+y)/2]-cos[(x-y)/2]}=-4sin[(x+y)/2]sin(x/2)sin(y/2),因x>0、y>0、0<x+y<2π,所以0<(x+y)/2<π、0<x/2<π、0<y/2<π,所以sin[(x+y)/2]>0、sin(x/2)>0、sin(y/2)>0,所以f(x)<0;因此远B恒小于零.
若x>0,y
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