Question

tan80°-tan20°-(根号3)tan80°tan20°=???

Answer 1

tan(80°-20°）=（tan80°-tan20°）/(1+tan80°tan20°)

tan80°-tan20°=(根号3)(1+tan80°tan20°)=根号3+(根号3)tan80°tan20°

tan80°-tan20°-(根号3)tan80°tan20°

=根号3+(根号3)tan80°tan20°-(根号3)tan80°tan20°

=根号3

Answer 2

tan(80°)=tan(20°+60°)=(tan20°+tan60°)/(1-tan20°tan60°)=(tan20+√3)/(1-√3tan20)
tan80-√3tan20tan80=tan20+√3
tan80-tan20-√3tan20tan80=√3

Answer 3

∵√3=tan60°=tan(80°-20°)=(tan80°-tan20°)/(1+tan80°tan20°)
∴√3+√3tan80°tan20°=tan80°-tan20°
∴tan80°-tan20°-√3tan80°tan20°=√3