Question

已知sina+sinb=1/2,cosa+cosb=1/3,请问cos(a-b)等于多少?

Answer 1

sina+sinb=1/2

(sina+sinb)^2=1/4

sina^2+2sinasinb+sinb^2=1/4(1)

cosa+cosb=1/3

(cosa+cosb)^2=1/9

cosa^2+2cosacosb+cosb^2=1/9(2)

(1)+(2):

2+2(cosacosb+sinasinb)=13/36

2+2cos(a-b)=13/36

2cos(a-b)=-59/36

cos(a-b)=-59/72