Question

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

Answer 1

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

都是口算,可能计算上会有点错~`

Answer 2

因sina-sinb= -1/3，所以（sina-sinb)^2=1/9
即sin^2a-2sina*sinb+sin^2b=1/9
所以sina*sinb=(sin^2a+sin^2b-1/9)
同理，cosa*cosb=(cos^2a+cos^2b-1/4)
cos(a-b)=cosa*cosb+sina*sinb
=sin^2a+sin^2b-1/9+cos^2a+cos^2b-1/4
=1+1-1/9-1/4
=59/36