(1+ sin2x)/(1+ cos2x+ sin2x)化简

(1+ sin2x)/(1+ cos2x+ sin2x)化简
(1+ sin2x)/(1+ cos2x+ sin2x)
化简

(1+ sin2x)/(1+ cos2x+ sin2x)化简
原式=(sinx+cosx)^2/[2(cosx)^2+2sinxcosx]
=(sinx+cosx)^2/2cosx(cosx+sinx)
=(sinx+cosx)/(2cosx)
=(1/2)(tanx+1)

cos^2 x+sin^2 x=1
于是：
原式=(cos^2 x+sin^2 x+ cos^2 x+ 2sinxcosx)/(cos^2 x+sin^2 x+ cos^2 x-sin^2 x+ 2sinxcosx)
=(cosx+sinx)^2/2cosx(cosx+ sinx)
=(cosx+sinx)/2cosx
=1/2+tanx/2