已知向量a=(cosx,sinx),向量b=(cosy,siny),若x-y=π/3,则向量a与向量a+b的夹角

已知向量a=(cosx,sinx),向量b=(cosy,siny),若x-y=π/3,则向量a与向量a+b的夹角

cosθ=a*(a+b)/|a|*|a+b|=(a^2+a*b)/|a+b|
=(1+a*b)/|a+b|
a*b=cosxcosy+sinxsiny
=cos(y-x)=cos(π/3)=1/2
|a+b|^2
=|a|^2+|c|^2+2a*b
=1+1+2*1/2
=3
∵cosθ=(1+1/2)/√3=√3/2
∴θ=π/6