b)
(tg\alpha+ctg\alpha)^2-5*sin\alpha*cos\alpha
(\frac{\sqrt5}{\sqrt2}+\frac{\sqrt2}{\sqrt5})^2-5*\frac{\sqrt5}{\sqrt7}*\frac{\sqrt2}{\sqrt7}=(\frac{(\sqrt5)^2+(\sqrt2)^2}{\sqrt2*\sqrt5})^2-5*\frac{\sqrt{10}}{7}=
=(\frac{5+2}{\sqrt{10}})^2-\frac{5\sqrt{10}}{7}=\frac{49}{10}-\frac{5\sqrt{10}}{7}=\frac{49*7-50\sqrt{10}}{70}=\frac{343-50\sqrt{10}}{70}
Czy zamiast -5 nie powinno być *5?
Wtedy sie to ładnie skróci:
\frac{49}{10}*\frac{5\sqrt{10}}{7}=\frac{7}{2}*\sqrt{10}=3,5\sqrt{10}