令sinx+cosx=t∈[-√2,√2]
(sinx+cosx)²=1+2sinxcosx
sinxcosx=(t²-1)/2
y=t²/2+t-1/2,t∈[-√2,√2]
开口向上,对称轴为t=-1
所以t=-1时,ymin=-1
t=√2时,ymax=√2+(1/2)