求证(1+sin2x)/(cosx+sinx)=cosx+sinx

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求证(1+sin2x)/(cosx+sinx)=cosx+sinx求证(1+sin2x)/(cosx+sinx)=cosx+sinx求证(1+sin2x)/(cosx+sinx)=cosx+sinx(

求证(1+sin2x)/(cosx+sinx)=cosx+sinx
求证(1+sin2x)/(cosx+sinx)=cosx+sinx

求证(1+sin2x)/(cosx+sinx)=cosx+sinx
(1+sin2x)/(cosx+sinx)
=(sin^2x+cos^2x+2sinxcosx)/(cosx+sinx)
=(cosx+sinx)^2/(cosx+sinx)
=cosx+sinx