求证：（1+sinx-cosx）/(1+sinx+cosx)=tan(x/2)

题目

求证：（1+sinx-cosx）/(1+sinx+cosx)=tan(x/2)

答案

证明：
(1+sinx-cosx)/(1+sinx+cosx)
= [(1-cosx)+sinx]/[(1+cosx)+sinx]
= {2*[sin(x/2)]^2+2sin(x/2)cos(x/2)}/{2*[cos(x/2)]^2+2sin(x/2)cos(x/2)}
= sin(x/2)/cos(x/2)
= tan(x/2)