已知tan(a+b)=7,tana·tanb=2/3,求cos(a-b)的值.

问题描述:

已知tan(a+b)=7,tana·tanb=2/3,求cos(a-b)的值.

tan(a+b)=(tana+tanb)/(1-tana*tanb),得到tana+tanb=7/3;tana+tanb=(sina/cosa)+(sinb/cosb)=(sinacosb+sinbcosa)/(cosa*cosb)=sin(a+b)/(cosa*cosb),tan(a+b)=7可得sin(a+b)=(+-)(7*√2)/10,所以cosa*cosb=(+-)(3*√2)/10,cos(a-b)=cosacosb+sinasinb=cosacosb(1+tanatanb)=(+-)(3*√2)/10×5/3=(+-)√2/2