Question

已知sin(a+b)=1/2,sin（a-b)=1/3,求tana/tanb

Answer 1

sin(a+b)=sinacosb+cossinb=1/2
sin(a-b)=sinacosb-cossinb=1/3
相加
2sinacosb=5/6
sinacosb=5/12
所以cosasinb=1/12
相除
(sina/cosa)/(sinb/cosb)=5
tana/tanb=5

Answer 2

sin(a+b)=sinacosb+cossinb=1/2
sin(a-b)=sinacosb-cossinb=1/3
sinacosb=5/12
cosasinb=1/12
tana/tanb=(sina/cosa)/(sinb/cosb)=(sinacosb)/(cosasinb)=5

Answer 3

sin(a+b)=sinacosb+cossinb=1/2
sin(a-b)=sinacosb-cossinb=1/3
相加
2sinacosb=5/6

(sina/cosa)/(sinb/cosb)=5