2sin(x-π/4)×sin(x+π/4)怎么化简成（sinx-cosx)(sinx+cosx),详细过程,谢谢了!

2sin(x-π/4)×sin(x+π/4)
=2sin(x-π/4)×sin[π/2-(π/4-x)]
=2sin(x-π/4)×cos(π/4-x)
=2sin(x-π/4)×cos(x-π/4)
=sin(2x-π/2)
=-cos2x
=-(cos^2x-sin^2x)
=-(cosx-sinx)(cosx+sinx)
=(sinx-cosx)(sinx+cosx)

(sinx-cosx)(sinx+cosx)可以化为sinx^2-cosx^2 然后化为cos2x 这是先从答案入手 再看已知条件可以化为2(sinxcos45-cosxsin45)(sinxcos45+cosxsin45) 裂开之后就是2(sinx^2cos45^2-cosx^2sin45^2) 而sin45^2等于cos45^2等于1/2 代入上式再根据我们对答案的分析就可以推出来了 手机党打字不容易啊 !