我就说算法,我不算
ab=cosαcos(π/4+α)+sinαcos(π/4-α)
=cosαcos(π/4+α)+sinαsin(π/4+α)
=cos[α-(π/4+α)]
=cosπ/4
=根号2/2
c^2
=(a+tb)^2
=a^2+t^2b^2+2tab
=cosα^2+sinα^2+t^2(cos(π/4+α)^2+sin(π/4+α)^2)+根号2t
=1+t^2+根号2t
=(t+根号2/2)^2+1/2
t=-根号2/2取最小,即1/2
|c|=根号c^2=根号2/2
剩下就很简单了,我不写了