向量a*b=1+(1+sina)(1+cosa)=1+1+(sina+cosa)+sinacosa
设t=sina+cosa=根号2sin(a+Pai/4)
Pai/4<=a<=Pai/2,Pai/2<=a+Pai/4<=3Pai/4
根号2/2<=sin(a+Pai/4)<=1
故有1<=t<=根号2.
sinacosa=(t^2-1)/2
所以有a*b=2+(t^2-1)/2+t=1/2(t^2+2t+1)+1=1/2(t+1)^2+1
在[1,根号2]上是单调增的,故有最大值是:1/2(3+2根号2)+1=根号2+5/2,最小值是:1/2*4+1=3