a-alfa,b-beta ------------------ Вычислите tg (a+b) u tg(a-b), если tga=1/3, tgb=1/5.

Решите задачу:

$tg(\alpha+\beta)=\frac{tg\alpha+tg\beta}{1-tg\alpha*tg\beta}=\frac{\frac{1}{3}+\frac{1}{5}}{1-\frac{1}{3}*\frac{1}{5}}=\frac{\frac{8}{15}}{\frac{14}{15}}=\frac{8}{14}=\frac{4}{7}\\\\\\tg(\alpha-\beta)=\frac{tg\alpha-tg\beta}{1+tg\alpha*tg\beta}=\frac{\frac{1}{3}-\frac{1}{5}}{1+\frac{1}{3}*\frac{1}{5}}=\frac{\frac{2}{15}}{\frac{16}{15}}=\frac{2}{16}=\frac{1}{8}$