方法一：
y=cosx+sinx
=(根2)*[(根2)/2*cosx+(根2)/2*sinx]
=(根2)*[sin(π/4)cosx+cos(π/4)sinx]
=(根2)*sin(x+π/4)
∵-1≤sin(x+π/4)≤1
∴-根2≤y≤根2
即函数y的极大值为“根2”,极小值为“-根2”
方法二：
cosx+sinx=y ……(1)
(cosx)^2+(sinx)^2=1 ……(2)
由(1)^2-(2)得
2sinxcosx=y^2-1
→sin2x=y^2-1
∵-1≤sin2x≤1
∴-1≤y^2-1≤1
解得,-根2≤y≤根2
即函数y的极大值为“根2”,极小值为“-根2”.对不起！y＝cosx－sinx＝－(sinx－cosx)＝－√2(sinx•√2/2－cosx•√2/2)＝－√2sin(x－π/4)∵－1≤sin(x－π/4)≤1∴－√2≤－√2sin(x－π/4)≤√2∴ymax=√2，ymin=－√2