Question

ПОМОГИТЕЕЕ

1. (tg a + ctg a) * sin a * cos a
2. sin^2 a * cos^2 a (tg^2 a + ctg^2 a + 2)

Answer 1

$(tg alpha +ctg alpha )cdot sin alpha cos alpha =tg alpha sin alpha cos alpha +ctg alpha sin alpha cos alpha =\ \ =sin^2 alpha +cos^2 alpha =1$


$sin^2 alpha cos^2 alpha (tg^2 alpha +ctg^2 alpha +2)=sin^2 alpha cos^2 alpha (tg alpha +ctg alpha )^2=\ \ =(tg alpha sin alpha cos alpha +ctg alpha sin alpha cos alpha )^2=(sin^2 alpha +cos^2 alpha )^2=1^2=1$