已知sin(a+b)等于2/3,sin(a-b0 =1/5,求tana:tanb

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已知sin(a+b)等于2/3,sin(a-b0=1/5,求tana:tanb已知sin(a+b)等于2/3,sin(a-b0=1/5,求tana:tanb已知sin(a+b)等于2/3,sin(a-

已知sin(a+b)等于2/3,sin(a-b0 =1/5,求tana:tanb
已知sin(a+b)等于2/3,sin(a-b0 =1/5,求tana:tanb

已知sin(a+b)等于2/3,sin(a-b0 =1/5,求tana:tanb
已知sin(a+b)等于2/3,sin(a-b0 =1/5
sin(a+b)/sin(a-b)
=(sina*cosb+cosa*sinb)/(sina*cosb-cosa*sinb)
分式上下同除以cosa*cosb
=(tana+tanb)/(tana-tanb)
=(tana/tanb+1)/(tana/tanb-1)
=(2/3)/(1/5)
所以tana/tanb=7/13
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sin(a+b)=sinacosb+cosasinb=2/3
sin(a-b)=sinacosb-cosasinb=1/5
两者相加:2sinacosb=13/15 sinacosb=13/30
两者相减:2cosasinb=7/15 cosasinb=7/30
tana:tanb=sinacosb:cosasinb=13/30:7/30=13:7