Question

已知tan110°=a，则tan50°=______

已知tan110°=a，则tan50°=______．

Answer 1

tan50°=tan（110°-60°）= tan110°-tan60° 1+tan110°tan60° = a- 3 1+ 3 a ． 故答案为： a- 3 1+ 3 a

Answer 2

tan110°=a
tan70°=－a
tan70°=tan(40°+30°)=(tan40°+tan30°)/(1-tan40°tan30°)=-a
(tan40°+tan30°)/(1-tan40°tan30°)=-a
(tan40°+√3/3)/(1-√3/3tan40°)=-a
(3tan40°+√3)/(3-√3tan40°)=-a
3tan40°+√3=-3a+√3atan40°
(√3a-3)tan40°=(3a+√3)
tan40°=(3a+√3)/(√3a-3)
tan50°=cot40°=1/tan40°=(√3a-3)/(3a+√3)=
tan50°=(√3a^2-4a+√3)/(3a^2-1)