Proszę o pomoc w przykładach g,h,i,j. Nie potrzebuję wszystkich, uciesze się z każdej pomocy.

f) [latex]frac{1+cosalpha}{sinalpha}=frac{sinalpha}{1-cosalpha}[/latex] [latex]L=frac{1+cosalpha}{sinalpha}=[/latex] [latex]frac{(1+cosalpha)(1-cosalpha)}{sinalpha(1-cosalpha)}=[/latex] [latex]frac{1-cos^2alpha}{sinalpha(1-cosalpha)}=[/latex] [latex]frac{sin^2alpha}{sinalpha(1-cosalpha)}=[/latex] [latex]frac{sinalpha}{1-cosalpha}=P[/latex] ================== g) [latex]left(frac{1}{cosalpha}-frac{1}{sinalpha} ight)cdot(1+tgalpha+ctgalpha)=frac{sinalpha}{cos^2alpha}-frac{cosalpha}{sin^2alpha}[/latex] [latex]L=left(frac{1}{cosalpha}-frac{1}{sinalpha} ight)cdot(1+tgalpha+ctgalpha)=[/latex] [latex]left(frac{1}{cosalpha}-frac{1}{sinalpha} ight)cdotleft(1+ frac{sinalpha}{cosalpha} + frac{cosalpha}{sinalpha} ight) =[/latex] [latex]frac{1}{cosalpha}+ frac{sinalpha}{cos^2alpha}+frac{1}{sinalpha}- frac{1}{sinalpha}- frac{1}{cosalpha} - frac{cosalpha}{sin^2alpha}=[/latex] [latex]frac{sinalpha}{cos^2alpha}-frac{cosalpha}{sin^2alpha}=P[/latex] ================== h) [latex]left(frac{1}{cosalpha}+frac{1}{sinalpha} ight)cdot(tgalpha+ctgalpha-1)=frac{sinalpha}{cos^2alpha}+frac{cosalpha}{sin^2alpha}[/latex] [latex]L=left(frac{1}{cosalpha}+frac{1}{sinalpha} ight)cdot(tgalpha+ctgalpha-1)=[/latex] [latex]left(frac{1}{cosalpha}+frac{1}{sinalpha} ight)cdotleft( frac{sinalpha}{cosalpha} + frac{cosalpha}{sinalpha} -1 ight) =[/latex] [latex]frac{sinalpha}{cos^2alpha}+frac{1}{sinalpha}- frac{1}{cosalpha}+frac{1}{cosalpha} + frac{cosalpha}{sin^2alpha} - frac{1}{sinalpha} =[/latex] [latex]frac{sinalpha}{cos^2alpha}+frac{cosalpha}{sin^2alpha}=P[/latex] ================== i) [latex](1+sinalpha)cdotleft(frac{1}{cosalpha}-frac{1}{ctgalpha} ight)-cosalpha=0[/latex] [latex]L=(1+sinalpha)cdotleft(frac{1}{cosalpha}-frac{1}{ctgalpha} ight)-cosalpha=[/latex] [latex](1+sinalpha)cdotleft(frac{1}{cosalpha}-frac{1}{ frac{cosalpha}{sinalpha} } ight)-cosalpha=[/latex] [latex](1+sinalpha)cdotleft(frac{1}{cosalpha}- frac{sinalpha}{cosalpha } ight)-cosalpha=[/latex] [latex]frac{1}{cosalpha}- frac{sinalpha}{cosalpha}+ frac{sinalpha}{cosalpha }- frac{sin^2alpha}{cosalpha} -cosalpha=[/latex] [latex]frac{1}{cosalpha}- frac{sin^2alpha}{cosalpha} -cosalpha=[/latex] [latex]frac{1-sin^2alpha}{cosalpha} -cosalpha=[/latex] [latex]frac{cos^2alpha}{cosalpha} -cosalpha=[/latex] [latex]cosalpha -cosalpha=0=P[/latex] ================== j) [latex](1-cosalpha)cdotleft(frac{1}{sinalpha}+frac{1}{tgalpha} ight)-sinalpha=0[/latex] [latex]L=(1-cosalpha)cdotleft(frac{1}{sinalpha}+frac{1}{tgalpha} ight)-sinalpha=[/latex] [latex](1-cosalpha)cdotleft(frac{1}{sinalpha}+frac{1}{ frac{sinalpha}{cosalpha} } ight)-sinalpha=[/latex] [latex](1-cosalpha)cdotleft(frac{1}{sinalpha}+frac{cosalpha}{sinalpha} ight)-sinalpha=[/latex] [latex]frac{1}{sinalpha}+frac{cosalpha}{sinalpha}- frac{cosalpha}{sinalpha}- frac{cos^2alpha}{sinalpha} -sinalpha=[/latex] [latex]frac{1}{sinalpha}- frac{cos^2alpha}{sinalpha} -sinalpha=[/latex] [latex]frac{1- cos^2alpha}{sinalpha} -sinalpha=[/latex] [latex]frac{sin^2alpha}{sinalpha} -sinalpha=[/latex] [latex]sinalpha -sinalpha=0=P[/latex]