求证：tan20tan40tan80的值等于tan60
问题描述：
求证：tan20tan40tan80的值等于tan60
答
tan20tan40tan80=tan20tan(60-20)tan(60+20) =tan20[(根号3-tan20)/(1+根号3tan20)][(根号3+tan20)/(1-根号3tan20)] =tan20[3-(tan20)^2]/[1-3(tan20)^2] =(sin20/cos20)[3(cos20)^2-(sin20)^2]/[(cos20)^2-3(sin20)...