Question

Пожалуйста, помогите

Answer 1

$frac{pi }{2}<alpha<pi \\alpha in2chetverti\\Cosalpha=-frac{sqrt{6} }{4}\\Sinalpha>0\\Sinalpha=sqrt{1-Cos^{2}alpha}=sqrt{1-(-frac{sqrt{6}}{4})^{2}}=sqrt{1-frac{6}{16} }=sqrt{frac{10}{16} }=frac{sqrt{10}}{4}\\tgalpha=frac{Sinalpha }{Cosalpha}=frac{sqrt{10} }{4}:(-frac{sqrt{6} }{4})=- frac{sqrt{10} }{4}*frac{4}{sqrt{6}}=-frac{sqrt{5} }{sqrt{3}}=-frac{sqrt{15} }{3}$

$Ctgalpha=frac{1}{tgalpha}=-frac{3}{sqrt{15}}=-frac{sqrt{15} }{5}$