Question

已知cos（a+b）=4/5，cos（a-b）=-3/5，求tanatanb的值

Answer 1

cos(a+b)=cosacosb-sinasinb=4/5
cos(a-b)=cosacosb+sinasinb=-3/5
联立方程求得cosacosb=1/10,sinasinb=-7/10
tanatanb=sinasinb/cosacosb=-7

Answer 2

cosacosb-sinasinb=4/5
cosacosb+sinasinb=-3/5
相加除2
cosacosb=1/10
相减除2
sinasinb=-7/10

tanatanb=(sina/cosa)*(sinb/cosb)
=sinasinb/cosacosb
=-7

Answer 3

tanatanb=sinasinb/(cosacosb)
sinasinb=0.5*[cos(a-b)-cos(a+b)]
cosacosb=0.5*[cos(a+b)+cos(a-b)]
代入，tanatanb=-7

Answer 4

cos(a+b) = cosacosb-sinasinb = 4/5 (1)
cos(a-b) = cosacosb+sinasinb = -3/5 (2)
联立(1)(2) 得出 cosa * cosb =
sina * sinb=
tana * tanb = (sina * sinb)/(cosa * cosb) =

Answer 5

把两个式子展开可得cosacosb-sinasinb=4/5 cosacosb+sinasinb=-3/5
可解得cosacosb=1/10 sinasinb=-7/10
所以tanatanb=(sinasinb)/(cosacosb)=-7

Answer 6

tanatanb=-7