3 zadania, TRYGONOMETRIA! DAJE 100 punktów.

[latex]frac{cos210^o sin330^o-sin210^o sin315^o}{0,25cdot(5sin^2150^o+2cos150^o sin225^o)}=[/latex] [latex]frac{cos(180^o+30^o) sin(270^o+60^o)-sin (180^o+30^o) sin(270^o+45^o)}{0,25cdot(5sin^2(180^o-30^o)+2cos(180^o-30^o) sin(180^o+45^o))}=[/latex] [latex]frac{-cos30^o (-cos60^o)+sin 30^o (-cos45^o)}{0,25cdot(5sin^230^o-2cos30^o(-sin45^o))}=[/latex] [latex]frac{cos30^o cos60^o-sin 30^o cos45^o)}{0,25cdot(5sin^230^o+2cos30^osin45^o)}=[/latex] [latex]frac{ frac{ sqrt{3} }{2} cdot frac{1}{2}- frac{1}{2} cdot frac{ sqrt{2} }{2} }{ frac{1}{4} cdotleft(5 cdot left( frac{1}{2} ight)^2 +2 cdot frac{ sqrt{3} }{2} cdot frac{ sqrt{2} }{2} ight) }=frac{ frac{ sqrt{3} }{4} -frac{ sqrt{2} }{4} }{ frac{1}{4} cdotleft(5 cdot frac{1}{4} + frac{ sqrt{6} }{2} ight) }=[/latex] [latex]frac{ frac{1}{4}left( sqrt{3} -sqrt{2} ight) }{ frac{1}{4} cdotleft(frac{5}{4} + frac{ sqrt{6} }{2} ight) }=frac{ sqrt{3} -sqrt{2} }{ frac{5}{4} + frac{ sqrt{6} }{2} }=frac{ sqrt{3} -sqrt{2} }{ frac{5}{4} + frac{2 sqrt{6} }{4} }=[/latex] [latex]frac{ sqrt{3} -sqrt{2} }{ frac{1}{4} cdotleft(5+ 2 sqrt{6} ight) }=4 cdot frac{ (sqrt{3} -sqrt{2})(5-2 sqrt{6}) }{(5+ 2 sqrt{6}) (5-2 sqrt{6})}=4 cdot frac{ 5sqrt{3} -2 sqrt{18}-5 sqrt{2}+2 sqrt{12}}{25-24}=[/latex] [latex]4 cdot frac{ 5sqrt{3} -6sqrt{2}-5 sqrt{2}+4sqrt{3}}{1}=4 cdot (9sqrt{3} -11sqrt{2})[/latex] ================ [latex]left(frac{1}{cosalpha}-cosalpha ight) left(frac{1}{sinalpha}-sinalpha ight) (tgalpha+ctgalpha)=1[/latex] [latex]L=left(frac{1}{cosalpha}-cosalpha ight) left(frac{1}{sinalpha}-sinalpha ight) (tgalpha+ctgalpha)=[/latex] [latex]left(frac{1}{cosalpha}- frac{cos^2alpha}{cosalpha} ight) left(frac{1}{sinalpha}- frac{sin^2alpha}{sinalpha} ight) (tgalpha+ctgalpha)=[/latex] [latex]left(frac{1- cos^2alpha}{cosalpha} ight) left(frac{1-sin^2alpha}{sinalpha} ight) (tgalpha+ctgalpha)=[/latex] [latex]frac{sin^2alpha}{cosalpha} cdot frac{cos^2alpha}{sinalpha}(tgalpha+ctgalpha)=[/latex] [latex]sinalpha cosalpha}left( frac{sinalpha}{cosalpha} + frac{cosalpha}{sinalpha} ight) =[/latex] [latex]sin^2alpha+cos^2alpha=1=P[/latex] ================ W załączniku