Oblicz wartość wyrażenia 3(4cos^2alfa -2) wiedząc, że ctgalfa=1/2 ?

[latex]hbox{ctg} alpha = frac{1}{2} \ hbox{ctg} alpha= frac{cos alpha}{sin alpha} \ frac{cos alpha}{sin alpha}=frac{1}{2} \ 2cos alpha=sin alpha \ \ hbox{Mamy jedynke trygonometryczna:} \ sin^{2} alpha+cos^{2}alpha = 1 \ hbox{podstawiamy pod} sin alpha hbox{wyrazenie} 2cos alpha: \ (2cos alpha)^{2}+cos^{2} alpha=1 \ 4cos^{2} alpha + cos^{2} alpha =1 \ 5cos^{2} alpha=1 quad /:5 \ cos^{2} alpha=frac{1}{5}[/latex] [latex]hbox{Zatem:} \ 3(4 cos^{2} alpha -2)=3 cdot (4 cdot frac{1}{5}-2)=3 cdot (frac{4}{5}-2)=3 cdot (-frac{6}{5})=-frac{18}{5}[/latex]