化简：根号〔(1+sina)/(1-sina）〕－根号〔(1-sina)/(1+sina)]

题目

化简：根号〔(1+sina)/(1-sina）〕－根号〔(1-sina)/(1+sina)]
其中a是第二象限的角

答案

1+sina=(sin(a/2))^2+(cos(a/2))^2+2sin(a/2)cos(a/2)
=(sin(a/2)+cos(a/2))^2
同理,1-sina=(sin(a/2)-cos(a/2))^2
原式=|（sina/2+cosa/2)/(sina/2-cosa/2)|-
|（sina/2-cosa/2)/(sina/2+cosa/2)|
通分,化简|(（sin+cos)^2-(sin-cos)^2)/(sin^2-cos^2)|
=4|sincos/(sin^2-cos^2)|=2|sina/cosa|=-2tana