Question

вычислите (cos^2альфа-sin^2альфа)^2+4sin^2альфаcos^2альфа

Answer 1

1)

$(cos(\alpha)^{2}-sin(\alpha)^{2})^{2}+4sin(\alpha)^{2}*cos(\alpha)^{2} \\ \\ cos(2\alpha)^{2}+4sin(\alpha)^{2}*cos(\alpha)^{2} \\ \\ cos(2\alpha)^{2}+sin(2\alpha)^{2}=1$

2)

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