Question

已知cosa+cosb=3/5,sina+sinb=4/5,则cos(a-b)

Answer 1

cosa+cosb=3/5.(1)

sina+sinb=4/5.(2)

(1)^2+(2)^2得

(cosa)^2+(cosb)^2+2cosacosb+(sina)^2+(sinb)^2+2sinasinb

=2+2cos(a-b)=(3/5)^2+(4/5)^2=1

∴cos(A-B)=-1/2