Question

Срочно
Докажите тождество (1-ctg a)^2+(1+ctg a)^2= 2(sin a)^-2

Answer 1

$(1-ctg alpha )^2+(1+ctg alpha )^2=2(sin alpha )^{-2}\ 1-2ctg alpha +ctg^2 alpha +1+2ctg alpha +ctg^2 alpha =2(sin alpha )^{-2}\ 2+2ctg^2 alpha =2(sin alpha )^{-2}\ 2(1+ctg^2 alpha )=2(sin alpha )^{-2}\ 2cdot frac{1}{sin^2 alpha } =2(sin alpha )^{-2}\ 2(sin alpha )^{-2}=2(sin alpha )^{-2}$