da minomic » 02/02/2013, 18:26
\[ \frac{1- \tan x}{1 + \tan x} \cdot \frac{1- \tan x}{1 + \tan x} = (2- \sqrt{3})^2 \]
\[ \left( \frac{1-\tan x}{1+\tan x} \right)^2 = (2- \sqrt{3})^2 \]
\[ \left( \frac{1-\tan x}{1+\tan x} \right) = \pm (2- \sqrt{3}) \]
$1^\circ$ caso:
\[ \left( \frac{1-\tan x}{1+\tan x} \right) = (2- \sqrt{3}) \Rightarrow \tan x = \frac{\sqrt{3}}{3} \Rightarrow x = \frac{\pi}{6} + k \pi \]
$2^\circ$ caso:
\[ \left( \frac{1-\tan x}{1+\tan x} \right) = -(2- \sqrt{3}) \Rightarrow \tan x = \sqrt{3} \Rightarrow x = \frac{\pi}{3} + k \pi \]
Ultima modifica di
minomic il 02/02/2013, 19:26, modificato 2 volte in totale.