已知a=(cosx+sinx,sinx),b=(cosx-sinx,2cosx),设f(x)=a*b.

解析：∵ a*b
=(cosx+sinx,sinx)*(cosx-sinx,2cosx)
=(cosx+sinx)(cosx-sinx)+2sinxcosx
=[(cosx)^2-(sinx)^2]+2sinxcosx
=cos2x+sin2x
=√2*sin(2x+π/4)
其最小正周期为 2π/2=π.
∵f(x)=√2*sin(2x+π/4)=√2*sin[2(x+π/8)]
y=sinx的图像---右移π/8个单位---纵坐标不变,横坐标缩短到原来的1/2-----
--横坐标不变,纵坐标扩大到原来的√2倍.
∵0≤x≤π/2,∴π/4≤2x+π/4≤5π/4
-√2/2≤sin(2x+π/4)≤1
∴f(x)max=√2,f(x)min=-1/2