由导数的定义:(cos(x))' = lim{t → 0} (cos(x+t)-cos(x))/t= lim{t → 0} -2sin(x+t/2)sin(t/2)/t (和差化积)= -lim{t → 0} sin(x+t/2) · lim{t → 0} sin(t/2)/(t/2) (极限四则运算)= -sin(x)·1 (sin(x)连续性,...