sina+cosa=k
(sina+cosa)^2=1+2sinacosa=k^2
sinacosa=(k^2-1)/2
(sina)^3+(cosa)^3=(sina+cosa)(sin^2a-sinacosa+cos^2a)=k(1-sinacosa)=k[1-(k^2-1)/2]
=k(3-k^2)/2<0
sina+cosa=√2sin(a+π/4)=k
-√2≤k≤√2
k^2≤2
3-k^2>0
k<0
k的取值范围是-√2≤k<0