Question

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

Answer 1

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