tan10tan70 / tan70-tan10+tan120

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tan10tan70 / tan70-tan10+tan120
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tan10tan70 / tan70-tan10+tan120
tan10tan70 / tan70-tan10+tan120

tan10tan70 / tan70-tan10+tan120
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