已知sinx-cosx= -4分之5 ，则sin2x的值等于 多少 已知sin(x+π/4)=-5/13,则sin2x的值等于?

\u5df2\u77e52sinx+cosx=4/5 \u6c42sin2x

\u89e3\u6790\uff1a2sinx+cosx=4/5
\u3000\u3000\u76f4\u63a5\u4f7f\u7528\u4e07\u80fd\u516c\u5f0f\uff1a
\u3000\u30002[2t/(1+t²)]+(1-t²)/(1+t²)=4/5
\u3000\u3000\u89e3\u5f97\uff0c
\u3000\u30005(4t+1-t²)=4(1+t²)
\u3000\u30009t²-20t-1=0
\u3000\u3000t=(20\u00b1\u221a436)/18
\u3000\u3000sin2x
\u3000\u3000=2*[2t/(1+t²)]*[(1-t²)/(1+t²)]
\u3000\u3000=4t(1-t²)/(1+t²)²
\u3000\u3000\u4ee3\u5165\u5373\u53ef~~
\u3000\u3000PS\uff1a\u6b64\u7c7b\u9898\u76ee\uff0c\u4e0d\u7ba1\u7528\u54ea\u79cd\u65b9\u6cd5\uff0c\u8ba1\u7b97\u91cf\u51e0\u4e4e\u90fd\u5dee\u4e0d\u591a

sin(\u03c0/4+x)=-5/13
sinxcos\u03c0/4+cosxsin\u03c0/4=-5/13
\u221a2/2(sinx+cosx)=-5/13
sinx+cosx = -5\u221a2/13
(sinx+cosx)^2 = (-5\u221a2/13)^2
sin^2x+cos^2x+2sinxcosx=50/169
1+sin2x=50/169
sin2x = -119/169

两边平方，得
1-2sinxcosx=25/16
-sin2x=9/16
sin2x=-9/16

(sinx-cosx)²=16/25=sin²x+cos²x-2sinxcosx=1-sin2x
∴sin2x=9/25

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