a+b=(cosa+cosb,sina+sinb)
a-b=(cosa-cosb,sina-sinb)
cos(a+b,a-b)=(a+b)*(a-b)/|a+b|*|a-b|
=[(cosa+cosb)(cosa-cosb)+(sina+sinb)(sina-sinb)]/√[(cosa+cosb)^2+(sina+sinb)^2]*√[(cosa-cosb)^2+(sina-sinb)^2]
=(cos^2 a -cos^2 b +sin^2 a -sin^2 b)/ √[(cosa+cosb)^2+(sina+sinb)^2]*√[(cosa-cosb)^2+(sina-sinb)^2]
=(1-1)/√[(cosa+cosb)^2+(sina+sinb)^2]*√[(cosa-cosb)^2+(sina-sinb)^2]
=0
所以夹角为90度