已知向量m=(cosa,sina)和向量n=（根号2-sina,cosa),a∈(π,2π）且|m+n|=8根号2/5,求cos(a/2,π/2）的值

m+n=(cosa-sina+√2,sina+cosa) ∴|m+n|=(cosa-sina+√2)+(sina+cosa)=(cosa-sina)+2√2(cosa-sina)+2+(cosa+sina) =2(sina+cosa)+2-2√2(sina-cosa)=2+2-4[(√2/2)sina-(√2/2)cosa]=4-4sin(a-π/2)=(8√2/5)=128/25 ∴sin(a-π/2)=-7/25 ∵a∈(π,2π) ∴a-π/2∈(π/2,3π/2) 而sin(a-π/2)0 sin(a-π/2)=cos(π/2-(a-π/2))=cos(π-a)=cos(a-π)=2cos(a/2-π/2)-1=-7/25 ∴cos(a/2-π/2)=9/25 ∴cos(a/2-π/2)=3/5