若(cosα-sinα)/(cosα+sinα)=4,则tan(π/4-α)等于

题目

若(cosα-sinα)/(cosα+sinα)=4,则tan(π/4-α)等于

答案

(cosα-sinα)/(cosα+sinα)=4分子分母同时除以cosα(1-tanα)/(1+tanα)=4∴ [tan(π/4)-tanα]/[1+tan(π/4)tanα]=4∴ tan(π/4-α)=4或者将tan(π/4-α)展开也可以tan(π/4-α)= [tan(π/4)-tanα]/[1+tan(π/4...