已知向量a=(cosa,sina),b={cosb,sinb},|a-b|=2√5/5
(1)求cos(a-b)
(2)若0<a<π/2,-π/2<b<0,且sinb=-5/13,求sina的值

向量a=(cosA,sinA),向量b=(cosB,sinB),|a-b|=2√5/5
1)a-b=(cosA-cosB,sinA-sinB)
--->|a-b|^2=(cosA-cosB)&2+(sinA-sinB)^2
=2-2(cosAcosB+sinAsinB)
=2-2cos(A-B)
|a-b}=2√5/5--->2-2cos(A-B)=4/5
--->cos(A-B)=3/5
2)0<A<pi/2,-pi/2<B<0--->0<A-B<pi
cos(A-B)=3/5--->sin(A-B)=4/5
sinB=-5/13--->cosB=12/13

sinA=sin[(A-B)+B]
=sin(A-B)cosB+cos(A-B)sinB
=4/5*12/13+3/5*(-5/13)
=33/65.