[tex]sin^2\alpha+cos^2\alpha=1\\sin^2\alpha=1-cos^2\alpha\\\\9cos^2\alpha-25sin^2\alpha=0\\9cos^2\alpha-25(1-cos^2\alpha)=0\\9cos^2\alpha-25+25cos^2\alpha=0\\34cos^2\alpha=25 /:34\\cos^2\alpha=\frac{25}{34}\\cos\alpha=\frac{5}{\sqrt{34}}=\frac{5\sqrt{34}}{34}\\\\sin^2\alpha=1-\frac{25}{34}\\sin^2\alpha=\frac9{34}\\sin\alpha=\frac{3}{\sqrt{34}}=\frac{3\sqrt{34}}{34}\\[/tex]
[tex]tg\alpha=\frac{3\sqrt{34}}{34}:\frac{5\sqrt{34}}{34}=\frac{3\sqrt{34}}{34}*\frac{34}{5\sqrt{34}}=\frac{3}5[/tex]
