[tex]cos\alpha=\frac{8}{17}\\\\\\\sqrt{tg^2\alpha+1}=\sqrt{\frac{sin^2\alpha}{cos^2\alpha}+1}=\\\\\sqrt{\frac{sin^2\alpha}{cos^2\alpha}+\frac{cos^2\alpha}{cos^2\alpha}}=\sqrt{\frac{sin^2\alpha+cos^2\alpha}{cos^2\alpha}}=\sqrt{\frac{1}{cos^2\alpha}}=\sqrt{\frac{1}{(\frac{8}{17})^2}}=\sqrt{\frac{17^2}{8^2}}=\frac{17}{8}=2\frac{1}{8}[/tex]
