Kąt alfa jest ostry i [latex]sin alpha = frac{1}{2cos alpha } [/latex] Oblicz wartość wyrażenia sin alfa + cos alfa

[latex]sin alpha = frac{1}{2cos alpha }[/latex] [latex]2sinalpha cosalpha=1[/latex] ---------------------------- [latex](sin alpha + cos alpha)^2=sin^2alpha+2sinalpha cosalpha+cos^2alpha[/latex] [latex](sin alpha + cos alpha)^2=1+2sinalpha cosalpha[/latex] [latex](sin alpha + cos alpha)^2=1+1[/latex] [latex](sin alpha + cos alpha)^2=2[/latex] [latex]sin alpha + cos alpha=sqrt2[/latex]