证明tan（阿尔法+四分之派）+tan（阿尔法+四分之三派）=2tan2阿尔法
问题描述：
证明tan（阿尔法+四分之派）+tan（阿尔法+四分之三派）=2tan2阿尔法
答
tan（a+π/4）+tan（a+3π/4）=tan（a+π/4）+tan（π/2+a+π/4）=tan（a+π/4）-cot（a+π/4）=sin(a+π/4)/cos(a+π/4)-cos(a+π/4)/sin(a+π/4)=(sin²(a+π/4)-cos²(a+π/4))/(sin(a+π/4)cos(a+π/4))...可以换种做法吗？cot老师没讲过...tan（a+π/4）+tan（a+3π/4）=(tana+tanπ/4)/(1-tana*tanπ/4)+(tana+tan3π/4)/(1-tana*tan3π/4)=(tana+1)/(1-tana)+(tana-1)/(1+tana)=((tana+1)²-(tana-1)²)/(1-tan²a)=(4tana)/((cos²a-sin²a)/cos²a)=4(sina/cosa)cos²a/cos2a=4(sinacosa)/cos2a=2sin2a/cos2a=2tan2a问下哦=(tana+1)/(1-tana)+(tana-1)/(1+tana)怎么算的呢?