作业帮求证：tan20tan40tan80的值等于tan60
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/15 09:06:14
求证：tan20tan40tan80的值等于tan60
求证：tan20tan40tan80的值等于tan60
求证：tan20tan40tan80的值等于tan60
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)^2]
=(sin20/cos20)[(2cos40+1)/(2cos40)-1]
=(sin60-sin20+sin20)/(cos60+cos20-cos20)
=tan60
或者：
tan20tan40tan80
=1/(8 sin70sin50sin10)
=1/(8*根号3/3/8)
=根号3
=tan60