1+√2
y=√(sinx+1)^2+(cosx+1)^2=√1+2sinx+(sinx)^2+1+2cosx+(cosx)^2=√(3+2(sinx+cosx)=√(3+2√2sin(x+45))
当x=45时取最大值 y=√(3+2√2)=1+√2