Question

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

Answer 1

$star ; ; cosfrac{pi}{12}=cos(frac{pi}{4}-frac{pi}{6})=cosfrac{pi}{4}cdot cosfrac{pi}{6}+sinfrac{pi}{4}cdot sinfrac{pi}{6}=frac{sqrt2}{2}cdot frac{sqrt3}{2}+frac{sqrt2}{2}cdot frac{1}{2}=\\=frac{sqrt6+sqrt2}{4}=frac{sqrt2cdot (sqrt3+1)}{4}=frac{sqrt3+1}{2sqrt2}; ; star \\\cosfrac{pi}{12}+cosfrac{pi}{4}+cosfrac{5pi}{6}=frac{sqrt6+sqrt2}{4}+frac{sqrt2}{2}-cos(pi -frac{pi}{6})=frac{sqrt6+sqrt2+2sqrt2}{4}+cosfrac{pi}{6}=$

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