Question

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

Answer 1

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