已知 cos(a+b)=1/3 ,cos(a-b)=1/5 ,则tan a 乘tan b 等于已知 cos(a+b)=1/3 ,c_数学解答

已知 cos(a+b)=1/3 ,cos(a-b)=1/5 ,则tan a 乘tan b 等于
已知 cos(a+b)=1/3 ,cos(a-b)=1/5 则tan a 乘tan b 等于
A1/4 B-1/4 C4 D -4

人气：321 ℃　时间：2020-04-30 03:47:47

解答

cos(a+b) = 1/3
cosa cos b - sina sinb = 1/3 ---(1)
cos(a-b)=1/5
cosa cosb + sina sinb = 1/5 ---(2)
(1) + (2)
2cosa cosb = 8/15 --(3)
(2) - (1)
2 sina sinb = -2/15 ---(4)
(4)/(3)
sinasinb/cosacosb = -1/4
tana.tanb = -1/4
ans :B