sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?

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sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?sin(a+b)=1/2,sin(a-b)=1/

sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?
sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?

sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?
sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?
sin(a+b)=sinacosb+cosasinb=1/2
sin(a-b)=sinacosb-cosasinb=1/3
联立--->sinacosb=5/12,cosasinb=1/12
相除--->tana/tanb=5

积化和差公式
sinacosb=[sin(a+b)+sin(a-b)]/2①
cosasinb=[sin(a+b)-sin(a-b)]/2②
①/②=tana*cotb
cotb=1/tanb
∴①/②=tana/tanb=(1/2+1/3)/(1/2-1/3)
=(5/6)/(1/6)
=5

2sin(a+b)=1,3sin(a-b)=1
∴2sin(a+b)=3sin(a-b)
2(sinacosb+sinbcosa)=3(sinacosb-sinbcosa)
2sinacosb+2sinbcosa=3sinacosb-3sinbcosa
5sinbcosa=sinacosb
两边同时除以cosacosb
5sinb/cosb=sina/cosa
5tanb=tana
tana/tanb=5

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