求（tan70°-tan10°+tan120°)/(tan70°tan10°)的值

tan70°-tan10°+ tan120°
-----------------------
tan70°tan10°
tan（70°－10°）（1＋tan70°tan10°）+tan120°
＝ ---------------------------------------------
tan70°tan10°
tan60°（tan70°tan10°+1）+ tan120°
＝ ----------------------------------------
tan70°tan10°
__
__ √3 + tan120°
= √3 ＋ ------------------
tan70°tan10°
__
__ √3 + tan(2×60°)
= √3 ＋ -------------------
tan70°tan10°
__ __
__ √3 -√3
= √3 ＋ -----------------
tan70°tan10°
__
= √3

tan6o°=tan(70°-10°)=(tan70°-tan10°)/(1-tan70°tan10)代入上式即可