[tex] \sqrt{72} * cos^{2} \frac{15 \pi }{8} - \sqrt{18} [/tex]. Created by Avrilkina. algebra-ru

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June 2022 1 8 Report

[tex] \sqrt{72} * cos^{2} \frac{15 \pi }{8} - \sqrt{18} [/tex]

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$\sqrt{71}\cdot cos^2\frac{15\pi}{8}-\sqrt{18}=\sqrt{72}\cdot cos^2(2\pi -\frac{\pi}{8})-\sqrt{18}=\\\\=\sqrt{72}\cdot cos^2\frac{\pi}{8}-\sqrt{18}=\sqrt{4\cdot 18}\cdot \frac{1+cos\frac{2\pi}{8}}{2}-\sqrt{18}=$

$=2\sqrt{18}\cdot \frac{1+cos\frac{\pi}{4}}{2}-\sqrt{18}=\sqrt{18}\cdot (1+\frac{\sqrt2}{2})-\sqrt{18}=\\\\=\sqrt{9\cdot 2}\cdot \frac{2+\sqrt2}{2}-\sqrt{9\cdot 2}=3\sqrt2\cdot (\frac{2+\sqrt2}{2}-1)=\\\\=3\sqrt2\cdot \frac{2+\sqrt2-2}{2}=3\sqrt2\cdot \frac{\sqrt2}{2}=3$

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