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PopAdrianid
[tex]\cos (arctg x)\\ y=arctg x \leftrightarrow tg y=x\\ \sin^2 y + \cos^2 y=1/ \cdot \frac{1}{\cos^2 y} \\ tg^2 y+1=\frac{1}{\cos^2 y} \\ x^2+1=\frac{1}{\cos^2 y} \\ |\cos y|=\sqrt{\frac{1}{x^2+1}} \\ \cos(\arctg x)=\sqrt{\frac{1}{x^2+1}} [/tex]

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