超簡單三角函數(急)!!!要求詳解

sina + sinb= √(3/2)
( sina + sinb ) ^ 2 = 3/2
sin^2 a + sin^2 b + 2sinasinb = 3/2 ...(1)

cosa + cosb = 3/2
( cosa + cosb ) ^ 2 = 9/4
cos^2 a + cos^2 b + 2cosacosb = 9/4...(2)

(1)+(2):
( sin^2 a + cos^2 a ) + ( sin^2 b +cos^2 b ) + 2( cosacosb + sinasinb ) = 15/4
2 + 2 ( cosacosb + sinasinb ) = 15/4
cosacosb + sinasinb = 7/8
cos(a-b) = 7/8 [By compound angle formula]