Question

Calculati tg 7pi/12.

Answer 1

Răspuns:

raspuns atasat

Answer 2

$\displaystyle \text{tg}\,\frac{7\pi}{12} = \text{tg}\left(\frac{3\pi}{12}+\frac{4\pi}{12}\right) = \text{tg}\left(\frac{\pi}{4}+\frac{\pi}{3}\right) = \frac{\text{tg}\,\frac{\pi}{4}+\text{tg}\,\frac{\pi}{3}}{1-\text{tg}\,\frac{\pi}{4}\cdot \text{tg}\,\frac{\pi}{3}} =$

$\displaystyle = \frac{1+\sqrt{3}}{1-1\cdot \sqrt{3}} = \frac{(1+\sqrt{3})^2}{1-3} =\frac{4+2\sqrt{3}}{-2} = \boxed{-2-\sqrt{3}}$