Question

已知sina+sinB=1/2,cosa+cosB=1/3,则cos(a-B)=

Answer 1

cosa+cosb=1/3 ,sina+sinb=1/2

分别两边平方

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

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

相加

且(cosa)^2+(sina)^2=1 (cosb)^2+(sinb)^2=1

2+2(cosacosb+sinasinb)=1/4+1/9=13/36

cos(a-b)=cosacosb+sinasinb

=(13/36-2)/2

=-59/72