sinx-cosx=根号2/2,则cosx+sinx的值为?

/>sinx-cosx=√2/2
两端平方
(sinx-cosx)²=(√2/2)²
sin²x+cos²x-2sinxcosx=1/2
1-2sinxcosx=1/2
sinxcosx=(1-1/2)/2=1/4
(cosx+sinx)²
=cos²x+sin²x+2sinxcosx
=1+2*1/4
=3/2
cosx+sinx=±√6/2
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