Question

cos П/12+ соs П/4 +cos 5П/6
Срочно! Помогите, подробно,пожалуйста

Answer 1

$\star \; \; cos\frac{\pi}{12}=cos(\frac{\pi}{4}-\frac{\pi}{6})=cos\frac{\pi}{4}\cdot cos\frac{\pi}{6}+sin\frac{\pi}{4}\cdot sin\frac{\pi}{6}=\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2}+\frac{\sqrt2}{2}\cdot \frac{1}{2}=\\\\=\frac{\sqrt6+\sqrt2}{4}=\frac{\sqrt2\cdot (\sqrt3+1)}{4}=\frac{\sqrt3+1}{2\sqrt2}\; \; \star \\\\\\cos\frac{\pi}{12}+cos\frac{\pi}{4}+cos\frac{5\pi}{6}=\frac{\sqrt6+\sqrt2}{4}+\frac{\sqrt2}{2}-cos(\pi -\frac{\pi}{6})=\frac{\sqrt6+\sqrt2+2\sqrt2}{4}+cos\frac{\pi}{6}=$

$=\frac{\sqrt6+3\sqrt2}{4}+\frac{\sqrt3}{2}=\frac{\sqrt6+3\sqrt2+2\sqrt3}{4}\; \; \; \Big [\; =\frac{3+\sqrt3+\sqrt6}{2\sqrt2}\; \Big ]$