Question

已知cosa+cosb=1/2，sina+sinb=1/3，求cos(a-b)的值？

Answer 1

(cosa+cosb)^2 + (sina+sinb)^2 = 2 + 2(cosacosb+sinasinb) = 1/4 + 1/9 = 13/36
而cos(a-b) = cosacosb + sinasinb
所以cos(a-b) = (13/36 - 2)/2 = -59/72

Answer 2

解：(cosa+cosb)²=(1/2)² (1)
(sina+sinb)²=(1/3)² (2)
(1)+(2)得：
sin²a+cos²a+sinb²+cos²b+2(cosa×cosb+sina×sinb)=1/4+1/9
1+1+2cos(a-b)=13/36
cos(a-b)=-59/72