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[tex]\displaystyle\bf\\Sin\alpha -Cos\alpha =-0,4\\\\\Big(Sin\alpha -Cos\alpha \Big)^{2} =\Big(-0,4\Big)^{2} \\\\Sin^{2} \alpha -2Sin\alpha Cos\alpha +Cos^{2} \alpha =0,16\\\\\underbrace{Sin^{2} \alpha +Cos^{2} \alpha}_{1} -\underbrace{2Sin\alpha Cos\alpha }_{Sin2\alpha }=0,16\\\\\\1-Sin2\alpha =0,16\\\\Sin2\alpha =1-0,16\\\\\boxed{Sin2\alpha =0,84}[/tex]

[tex]\sin \alpha -\cos \alpha =-0.4\\(\sin \alpha -\cos \alpha)^{2} =0.16\\\sin \alpha^{2} +\cos \alpha^{2}-2\sin \alpha \cos \alpha=0.16\\1-\sin 2\alpha=0.16\\1-0.16=\sin 2\alpha\\\sin 2\alpha=0.84[/tex]Ответ:0.84

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