Matematyka

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krystian01239

[latex]c=sqrt{(3sqrt{2})^2+(sqrt{6})^2}=sqrt{18+6}=sqrt{24}=2sqrt{6}\ \ a) frac{cos alpha -sin alpha }{sin alpha }=frac{frac{sqrt{6}}{2sqrt{6}} - frac{3sqrt{2}}{2sqrt{6}}}{frac{3sqrt{2}}{2sqrt{6}}}=frac{frac{sqrt{6}-3sqrt{2}}{2sqrt{6}}}{frac{3sqrt{2}}{2sqrt{6}}}=frac{sqrt{6}-3sqrt{2}}{2sqrt{6}}cdot frac{2sqrt{6}}{3sqrt{2}}=\=frac{sqrt{2}(sqrt{3}-3)}{3sqrt{2}}=frac{sqrt{3}-3}{3}\ \ [/latex] [latex]b) frac{sin alpha +cos eta }{3tg alpha +1}cdot tg eta = frac{frac{3sqrt{2}}{sqrt{6}}+frac{3sqrt{2}}{sqrt{6}}}{3cdot frac{sqrt{2}}{sqrt{6}}+1}cdot frac{sqrt{6}}{3sqrt{2}}=frac{frac{6sqrt{2}}{sqrt{6}}}{frac{3sqrt{2}+sqrt{6}}{sqrt{6}}}cdot frac{sqrt{6}}{3sqrt{2}}=\ [/latex] [latex]=frac{6sqrt{2}}{sqrt{6}}cdot frac{sqrt{6}}{3sqrt{2}+sqrt{6}}}cdot frac{sqrt{6}}{3sqrt{2}}=frac{6sqrt{2}}{3sqrt{2}+sqrt{6}}}cdot frac{sqrt{3}}{3}=frac{6sqrt{2}}{sqrt{2}(3+sqrt{3})}cdot frac{sqrt{3}}{3}=\=frac{2sqrt{3}}{3+sqrt{3}} cdot frac{3-sqrt{3}}{3-sqrt{3}}=frac{6sqrt{3}-6}{9-3}=frac{6(sqrt{3}-1)}{6}=sqrt{3}-1[/latex] [latex]c) frac{sin^2 alpha +cos^2 eta }{sin alpha cos eta }cdot tg alpha =frac{(frac{3sqrt{2}}{2sqrt{6}})^2+(frac{3sqrt{2}}{2sqrt{6}})^2}{frac{3sqrt{2}}{2sqrt{6}}cdot frac{3sqrt{2}}{2sqrt{6}}} cdot frac{3sqrt{2}}{sqrt{6}} = \=frac{frac{18}{24}+frac{18}{24}}{frac{18}{24}}cdot frac{3}{sqrt{3}}=frac{frac{36}{24}}{frac{18}{24}}cdot frac{3}{sqrt{3}}=frac{36}{24}cdot frac{24}{18}cdot frac{3}{sqrt{3}} = frac{6}{sqrt{3}}=frac{6sqrt{3}}{3}=2sqrt{3}[/latex]

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Matematyka

Prosze o rozwiazanie zadania z zalacznika.