(1+2sinxcosx+cos^2x-sin^2x)+1这个是怎么到这步的[(cosx+sinx)(cosx+sinx+cosx-sinx]+1?用了哪个公式?

问题描述:

(1+2sinxcosx+cos^2x-sin^2x)+1这个是怎么到这步的[(cosx+sinx)(cosx+sinx+cosx-sinx]+1?用了哪个公式?

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)]...倒数第二步[(cosx+sinx)²+(cosx-sinx)(cosx+sinx)]+1是怎么到[(cosx+sinx)(cosx+sinx+cosx-sinx)]+1?[(cosx+sinx)²+(cosx-sinx)(cosx+sinx)]+1是怎么到[(cosx+sinx)(cosx+sinx+cosx-sinx)]+1?在中括弧内取公因式(cosx+sinx)