2.
а)
1-sin^2 α =cos^2 α
ctg^2 α =cos^2 α /sin^2 α
ctg^2 α * sin^2 α =cos^2 α
1-sin^2 α +ctg^2 α *sin^2 α =2cos^2 α
б) 1-ctg^2 α =1-(cos^2 α/sin^2 α) =(sin^2 α -cos^2 α )/sin^2 α
1/(1-ctg^2 α )=sin^2 α /(sin^2 α -cos^2 α )
1+ tg^2 α =1-(sin^2 α /cos^2 α )=(cos^2 α -sin^2 α )/cos^2 α
1/(1+tg^2 α)=cos^2 α /(cos^2 α -sin^2 α )
О т в е т. sin^2 α /(sin^2 α -cos^2 α ) + cos^2 α /(cos^2 α -sin^2 α )=
=sin^2 α /(sin^2 α -cos^2 α ) - cos^2 α /(sin^2 α -cos^2 α ) =
=(sin^2 α -cos^2 α ) /(sin^2 α -cos^2 α ) =1