Question

tg альфа + ctg альфа,если sin альфа cos альфа=0.6

Answer 1

$tg(\alpha)+ctg(\alpha)=tg(\alpha)+ \frac{1}{tg(\alpha)} = \frac{tg(\alpha)^{2}+1}{tg(\alpha)} \\ \\ \frac{ \frac{sin(\alpha)^{2}}{cos(\alpha)^{2}}+1 }{ \frac{sin(\alpha)}{cos(\alpha)} } = \frac{ \frac{sin(\alpha)^{2}+cos(\alpha)^{2}}{cos(\alpha)^{2}} }{ \frac{sin(\alpha)}{cos(\alpha)} } = \frac{1}{cos(\alpha)*sin(\alpha)} = \frac{1}{0,6}= \frac{1}{ \frac{5}{3} } = \frac{5}{3}=1 \frac{2}{3}$