sinx+cosx=√2(√2/2sinx+√2/2cosx)
=√2(sinxcos45°+cosx+sin45°)
= √2 sin(x+45°)=m
sin(x+45°)= √2/2 m
因为-1≤ sinα≤1
所以 -1≤√2/2 m≤1
-√2≤m≤√2
当m=√2时,
sin(x+45°)= 1
x+45°=2kл+л/2 （k=0,1,2,3,.)
x=2kл+л/4
y=sinx+cosx+2sinxcosx+2
=sinx+cosx+2sinxcosx+sinx^2+cosx^2+1
=(sinx+cosx)^2+(sinx+cosx)+1
=(sinx+cosx)^2+(sinx+cosx)+1/4+3/4
=(sinx+cosx+1/2)^2+3/4
=(√2sin(x+л/4)+1/2)^2+3/4
-1