已知:sin(a+b)=2/3,sin(a-b)=2/5,求(tana-tanb)/(tana+tanb)的值.

问题描述:

已知:sin(a+b)=2/3,sin(a-b)=2/5,求(tana-tanb)/(tana+tanb)的值.

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