f（x）=1+sinx-cosx/1+sinx+cosx 怎么化简 要有详细步骤哦
问题描述：
f（x）=1+sinx-cosx/1+sinx+cosx 怎么化简 要有详细步骤哦
如题拜托啦
答
f(x)=(1-cosx +sinx)/(1+cosx+sinx)
=[2sin²(x/2)+2sin(x/2)cos(x/2)]/[2cos²(x/2)+2sin(x/2)cos(x/2)]
=2sin(x/2)[sin(x/2)+cos(x/2)]/2cos(x/2)[cos(x/2)+sin(x/2)]
=sin(x/2)/cos(x/2)
=tan(x/2)