oblicz wartość wyrażenia sin alfa +cos alfa * ctg alfa , jesli alfa jest katem ostrym a tg alfa =1/4

[latex]tg alpha =frac{1}{4}\ frac{sin alpha }{cos alpha }=frac{1}{4} \ sin alpha =frac{1}{4}cos alpha \ \ sin^2 alpha +cos^2 alpha =1\ (frac{1}{4}cos alpha )^2+cos^2 alpha =1\ frac{1}{16}cos^2 alpha +cos^2 alpha =1\ frac{17}{16}cos^2 alpha =1\ cos^2 alpha =frac{16}{17}\ cos alpha =sqrt{frac{16}{17}} = frac{4}{sqrt{17}} = frac{4sqrt{17}}{17}\ \ sin alpha =frac{1}{4}cdot frac{4sqrt{17}}{17}= frac{sqrt{17}}{17}\ \ [/latex] [latex]ctg alpha =frac{1}{tg alpha }=frac{1}{frac{1}{4}}=4\ \ \ sin alpha +cos alpha cdot ctg alpha =frac{sqrt{17}}{17}+frac{4sqrt{17}}{17}cdot 4 = \=frac{sqrt{17}}{17} + frac{16sqrt{17}}{17}=frac{17sqrt{17}}{17}=sqrt{17}[/latex]