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

问题描述:

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

cosx=cos2 x/2 - sin2 x/2,sinx=2sinx/2 * cosx/2,
原式=(2sin2 x/2 +2sinx/2*cosx/2)/(2cos2 x/2 + 2sinx/2*cosx/2)=tan x/2