[tex]tg\alpha=5\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}\\25=\frac{1-cos^2\alpha}{cos^2\alpha}\\25cos^2\alpha=1-cos^2\alpha\\26cos^2\alpha=1 /:26\\cos^2\alpha=\frac1{26}\\cos\alpha=\frac{\sqrt{26}}{26}\\\\sin^2\alpha=1-\frac1{26}\\sin^2\alpha=\frac{25}{26}\\sin\alpha=\frac{5\sqrt{26}}{26}[/tex]
[tex]sin\alpha-cos\alpha=\frac{5\sqrt{26}}{26}-\frac{\sqrt{26}}{26}=\frac{4\sqrt{26}}{26}=\frac{2\sqrt{26}}{13}\\sin\alpha+cos\alpha=\frac{5\sqrt{26}}{26}+\frac{\sqrt{26}}{26}=\frac{6\sqrt{26}}{26}=\frac{3\sqrt{26}}{13}\\\\\frac{sin\alpha-cos\alpha}{sin\alpha+cos\alpha}=\frac{2\sqrt{26}}{13}*\frac{13}{3\sqrt{26}}=\frac{2\sqrt{26}}{3\sqrt{26}}=\frac23[/tex]
