Oblicz wartość wyrażenia sin a * cos a + ctg a, wiedząc, że tg =2 i 0 < a < 90 (czyli pierwsza ćwiartka, jest dodatki)

[latex]tg alpha =2\ frac{sin alpha }{cos alpha }=2\ sin alpha =2cos alpha \ \ sin^2 alpha +cos^2 alpha =1\ (2cos alpha )^2+cos^2 alpha =1\ 4cos^2 alpha +cos^2 alpha =1\ 5cos62 alpha =1\ cos^2 alpha =frac{1}{5}\ cos alpha = sqrt{frac{1}{5}}=frac{sqrt{5}}{5}\ \ sin alpha =2cdot frac{sqrt{5}}{5}=frac{2sqrt{5}}{5}\ \ ctg alpha =frac{1}{tg alpha }=frac{1}{2}\ \ [/latex] [latex]sin alpha cdot cos alpha +ctg alpha =frac{2sqrt{5}}{5}cdot frac{sqrt{5}}{5}+frac{1}{2}=frac{2}{5}+frac{1}{2}=frac{9}{10}=0,9[/latex]