[latex]frac{3 sin alpha}{sin (90^o + alpha)}+ frac{cos alpha}{sin(90^o -alpha)}=2[/latex] [latex]frac{3 sin alpha}{cosalpha}+ frac{cos alpha}{cosalpha}=2[/latex] [latex]3tgalpha+1=2[/latex] [latex]3tgalpha=2-1[/latex] [latex]3tgalpha=1[/latex] [latex]tgalpha= frac{1}{3} [/latex] _________________ [latex]ctgalpha= frac{1}{tgalpha}[/latex] [latex]ctgalpha= frac{1}{frac{1}{3}}[/latex] [latex]ctgalpha=3[/latex] ________________ [latex]tg alpha +ctg alpha=frac{1}{3}+3=3 frac{1}{3} [/latex]
α - kąt ostry [latex]frac{3sin alpha}{sin(90^o + alpha)} + frac{cos alpha}{sin(90^o - alpha)} = 2 \\ frac{3sin alpha}{cos alpha} + frac{cos alpha}{cos alpha} = 2 \\ 3 cdot frac{sin alpha}{cos alpha} +1= 2 \\ 3 cdot tg alpha = 2 - 1\\ 3 cdot tg alpha = 1 /: 3 \\ tg alpha =frac{1}{3} \\ ctg alpha =frac{1}{tg alpha} \\ ctg alpha =frac{1}{frac{1}{3}} \\ ctg alpha = 3[/latex] Zatem: [latex]tg alpha + ctg alpha = frac{1}{3} + 3 = 3frac{1}{3}[/latex]
