[latex]tgalpha = 4\\\ dfrac {sinalpha}{cosalpha} = 4 o sinalpha = 4cosalpha o sin^2alpha = 16 cos^2 alpha \\\ sin^2 + cos ^2 alpha = 1 o sin^2alpha = 1-cos^2 alpha\\ 16cos^2alpha = 1-cos^2 alpha\\ 17cos^2alpha =1\\ cos^2alpha = dfrac 1{17} cosalpha = pmsqrt{dfrac1{17}} \\ [/latex] [latex]sin^2alpha = 1- cos^2alpha = 1-dfrac 1{17} = dfrac {16}{17} sinalpha = pm sqrt {dfrac{16}{17}}[/latex] [latex]dfrac {sinalpha} {cosalpha} extgreater 0 o sinalpha cdot cosalpha extgreater 0[/latex] [latex]dfrac{2 sin^2alpha - 3 sinalpha cosalpha}{ cosalpha - 7 cos^2alpha } = dfrac{2 cdot frac {16}{17} - 3 cdot sqrt{frac {16}{17}} cdot sqrt{frac {1}{17}}}{3 cdot sqrt{frac {16}{17}} cdot sqrt{frac {1}{17}} - 7 cdot frac{1}{17} } = dfrac {frac {32}{17}-3sqrt{frac{16}{17^2}}}{3sqrt{frac{16}{17^2}} - frac 7{17}}= \\\ =dfrac{frac{32}{17}-3cdot frac 4{17}}{3cdot frac 4{17} - frac 7{17}}=dfrac{frac{32}{17}- frac {12}{17}}{ frac {12}{17} - frac 7{17}}=dfrac{20}5 =4[/latex]
[latex]dfrac{2sin^2alpha-3sinalphacosalpha}{3sinalphacosalpha-7cos^2alpha} = dfrac{sinalpha(2sinalpha-3cosalpha)}{cosalpha(3sinalpha-7cosalpha)} = \= analphacdotdfrac{2sinalpha-3cosalpha}{3sinalpha-7cosalpha} = analphacdotdfrac{cosalpha(2frac{sinalpha}{cosalpha}-3)}{cosalpha(3frac{sinalpha}{cosalpha}-7)} = [/latex] [latex]= analphacdotdfrac{2frac{sinalpha}{cosalpha}-3}{3frac{sinalpha}{cosalpha}-7} = analphacdotdfrac{2 analpha-3}{3 analpha-7} = 4cdotdfrac{2cdot4-3}{3cdot4-7} = \=4cdotdfrac{5}{5}=4[/latex]
