证明(1+sinx)/(1+sinx+cosx)=(1/2)(1+tanx/2)

问题描述:

证明(1+sinx)/(1+sinx+cosx)=(1/2)(1+tanx/2)

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.