Oblicz ( trygonometria ) zadanie w załączniku, proszę o wytłumaczenie podanych przykładów

[latex]1+tg^2alpha=1+frac{sin^2alpha}{cos^2alpha}=frac{sin^2alpha+cos^2alpha}{cos^2alpha}=frac{1}{cos^2alpha}\\ frac{cosalpha}{tgalpha}-frac{1}{sinalpha}=cosalpha*frac{sinalpha}{cosalpha}-frac{1}{sinalpha}=sinalpha-frac{1}{sinalpha}=frac{sin^2alpha-1}{sinalpha}=\=frac{-cos^2alpha}{sinalpha}=-ctgalpha*cosalpha\\ frac{1-cos^2alpha}{tg^2alpha}=sin^2alpha*frac{cos^2alpha}{sin^2alpha}=cos^2alpha\\ [/latex] [latex]frac{1}{cosalpha}-sinalpha*tgalpha=frac{1}{cosalpha}-sinalpha*frac{sinalpha}{cosalpha}=frac{1}{cosalpha}-frac{sin^2alpha}{cosalpha}=frac{1-sin^2alpha}{cosalpha}=\ =frac{cos^2alpha}{cosalpha}=cosalpha[/latex]