sin(a+b)=1/3,sin(a-b)=1/5,则tana*cotb=?

问题描述:

sin(a+b)=1/3,sin(a-b)=1/5,则tana*cotb=?

sin(a+b)=sinαcosb+cosαsinb=1/3
sin(a-b)=sinαcosb-cosαsinb=1/5
俩个式子相加 sinαcosb+cosαsinb+sinαcosb-cosαsinb=2sinαcosb=8/15
俩个式子相减 sinαcosb+cosαsinb-sinαcosb+cosαsinb=2cosαsinb=2/15
得出 2sinαcosb=8/15,2cosαsinb=2/15
再相除 2sinαcosb/2cosαsinb=tana*cotb=4