证：(1+sinx)/(1+sinx+cosx)
=(1+2sinx/2 cosx/2)/(1+2sinx/2 cosx/2+2cos²x/2-1)
=(sin²x/2+cos²x/2+2sinx/2 cosx/2)/(2sinx/2 cosx/2+2cos²x/2)
=（sinx/2+cosx/2）²/[2cosx/2 (sinx/2+cosx/2)]
=（sinx/2+cosx/2）/(2cosx/2)
=(1/2)(1+tanx/2) 证毕.