y=sinxcosx+sinx+cosx+1
令a=sinx+cosx=√2sin(x+π/4)
0π/4所以√2/2所以1a²=sin²x+cosx²+2sinxcosx=1+2sinxcosx
所以sinxcosx=(a²-1)/2
所以y=(a²-1)/2+a+1=a²/2+a+1/2=1/2(a+1)²
12所以y最大值=1/2(√2+1)²=(3/2)+√2