(1+2sinxcosx+cos^2x-sin^2x)+1这个是怎么到这步的[(cosx+sinx)

网友回答

解由(1+2sinxcosx+cos^2x-sin^2x)+1
=(cos^2x+sin^2x+2sinxcosx+cos^2x-sin^2x)+1
=(cos^2x+2sinxcosx+sin^2x+cos^2x-sin^2x)+1
=[(cosx+sinx)²+cos^2x-sin^2x]+1
=[(cosx+sinx)²+（cosx-sinx）（cosx+sinx）]+1
=[(cosx+sinx)（cosx+sinx+cosx-sinx）]+1