Question

ctg(1/2arccos(-1/3)) срооочно плз помогите !!)))

Answer 1

$ctg(frac{arccos(-frac{1}{3})}{2})\ ctgfrac{a}{2} = frac{1+cosa}{sina}=frac{1+cos*(arccos(-frac{1}{3}))}{sina(arccos(-frac{1}{3}))}=\ arccos(-frac{1}{3})=x\ cosx= - frac{1}{3}\ sinx=sqrt{1-frac{1}{9}}=frac{sqrt{8}}{3}\ x=arcsin(frac{sqrt{8}}{3})\ ctg(frac{arccos(-frac{1}{3})}{2}) = frac{ 1-frac{1}{3}}{frac{sqrt{8}}{3}} = frac{2}{sqrt{8}}=frac{sqrt{2}}{2}$