Question

Упростите выражения
1) (1+ ctg²α) · sin²α +1;
2) (tgα · ctgα - cos²α) · 1/sin²α; 
3) tgα · ctgα + sinα.

Answer 1

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