Question

CosП/12*cosП/4

Хелп миииииии

Answer 1

$cos\frac{\pi}{12}\cdot cos\frac{\pi }{4}=\frac{1}{2}\cdot (cos(\frac{\pi}{12}+\frac{\pi}{4})+cos(\frac{\pi}{12}-\frac{\pi}{4}))=\\\\=\frac{1}{2}\cdot (cos\frac{\pi}{3}+cos(-\frac{\pi}{6}))=\frac{1}{2}\cdot (\frac{1}{2}+cos\frac{\pi }{6} )=\frac{1}{2}\cdot (\frac{1}{2}+\frac{\sqrt3}{2})=\\\\=\frac{1}{2}\cdot \frac{1+\sqrt3}{2}=\frac{1+\sqrt3}{4}\\\\ili\\\\cos\frac{\pi}{12}\cdot cos\frac{\pi }{4}=\frac{\sqrt6+\sqrt2}{4}\cdot \frac{\sqrt2}{2}=\frac{\sqrt2\cdot (\sqrt3+1)\cdot \sqrt2}{4\cdot 2}=\frac{2\cdot (\sqrt3+1)}{4\cdot 2}=\frac{1+\sqrt3}{4}$