12. 5 tg arccos 1/3

1) $$arccos(\frac{1}{3}) = a$$

2) $$tg(arccos(\frac{1}{3})) = tg(a) = \frac{sin(a)}{cos(a)}$$

3) $$cos(a) = \frac{1}{3}$$

4) $$sin(a) = \sqrt{1 - cos^2(a)} = \sqrt{1 - (\frac{1}{3})^2} = \sqrt{1 - \frac{1}{9}} = \sqrt{\frac{8}{9}} = \frac{2\sqrt{2}}{3}$$

5) $$\frac{sin(a)}{cos(a)} = \frac{\frac{2\sqrt{2}}{3}}{\frac{1}{3}} = 2\sqrt{2}$$

6) $$5 \cdot 2\sqrt{2} = 10\sqrt{2}$$

Ответ: $$10\sqrt{2}$$