Question

1. $frac{sin alpha -cos alpha }{sin alpha +cos alpha }$ ,tgальфа=$frac{2}{5}$
2.$frac{tg alpha }{ctg alpha } +tg beta ctg beta$

Answer 1

$1.; frac{sin alpha -cos alpha }{sin alpha +cos alpha }=frac{frac{sin alpha -cos alpha }{cos alpha }}{frac{sin alpha +cos alpha }{cos alpha }}=frac{tg alpha -1}{tg alpha +1}=frac{frac{2}{5}-1}{frac{2}{5}+1}=frac{2-5}{2+5}=-frac{3}{7}\\2.; frac{tg alpha }{ctg alpha }+tg beta cdot ctg beta =frac{tg alpha }{frac{1}{tg alpha }}+1=tg^2 alpha +1=frac{1}{cos^2 alpha }$