设α+β=π/3,tanα+tanβ=3,则cosαcosβ=

题目

设α+β=π/3,tanα+tanβ=3,则cosαcosβ=

答案

　　tana+tanb=3
sina/cosa+sinb/cosb=3
(sinacosb+sinbcosa)/cosacosb=3
sin(a+b)/cosacosb=3
sin(派/3)/cosacosb=3
(根号3)/2=3cosacosa
cosacosb=(根号3)/6.