[tex](\sin \alpha+\cos\alpha)^2+(\sin \alpha-\cos\alpha)^2=\\\sin^2\alpha+2\sin \alpha\cos\alpha +\cos^2\alpha+\sin^2\alpha-2\sin \alpha\cos\alpha +\cos^2\alpha=\\1+1=1[/tex]
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[tex](a+b)^2=a^2+2ab+b^2\\(a-b)^2=a^2-2ab+b^2\\\sin^2\alpha+\cos^2\alpha=1[/tex]
