tan(4分之派－阿尔发）＝3,则cot阿尔发＝?

题目

tan(4分之派－阿尔发）＝3,则cot阿尔发＝?
知道的说下,

答案

tan(π/4-α)
=(tanπ/4-tanα)/(1+tanπ/4tanα)
=(1-tanα)/(1+tanα)=3
1-tanα=3+3tanα
tanα=-1/2
cotα=1/tanα=-2