[tex]sin\alpha+cos\alpha=\frac{\sqrt{35}}{5}}\ \ \ |()^2\\\\sin^2\alpha+2sin\alpha cos\alpha+cos^2\alpha=\frac{35}{25}\\\\1+2 sin\alpha cos\alpha=\frac{7}{5}\\\\2 sin\alpha cos\alpha=\frac{7}{5}-1\\\\2 sin\alpha cos\alpha=\frac{2}{5}\ \ \ |:2\\\\ sin\alpha cos\alpha=\frac{1}{5}[/tex]
[tex]tg\alpha+ctg\alpha=\frac{sin\alpha}{cos\alpha}+\frac{cos\alpha}{sin\alpha}=\frac{sin^2\alpha+cos^2\alpha}{sin\alpha cos\alpha}=\frac{1}{sin\alpha cos\alpha}=\frac{1}{\frac{1}{5}}=5[/tex]
