[tex]0^{o} < \alpha < 90^{o}\\tg\alpha = 3\\\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\\\3 = \frac{sin\alpha}{cos\alpha}\\\\sin\alpha = 3 cos\alpha\\\\Z \ jedynki \ trygonometrycznej:\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\\\(3cos\alpha)^{2}+cos^{2}\alpha = 1\\\\9cos^{2}\alpha +cos^{2}\alpha = 1\\\\10 cos^{2}\alpha = 1 \ \ /:10\\\\cos^{2} \alpha = \frac{1}{10}\\\\cos\alpha = \sqrt{\frac{1}{10}} = \frac{1}{\sqrt{10}}\cdot\frac{\sqrt{10}}{\sqrt{10}} =\frac{\sqrt{10}}{10}[/tex]
[tex]sin\alpha = 3 cos\alpha = \frac{3\sqrt{10}}{10}\\\\sin\alpha + cos \alpha = \frac{3\sqrt{10}}{10} + \frac{\sqrt{10}}{10} = \frac{4\sqrt{10}}{10} = \frac{2\sqrt{10}}{5}\\\\\boxed{sin\alpha + cos\alpha = \frac{2\sqrt{10}}{5}}[/tex]
