Question

exercițiul 6 cu funcții trigonometrice

Answer 1

Răspuns:

$\frac{\sqrt3}{3}$

Explicație pas cu pas:

Stim ca:

$tg(a-b)=\frac{tga-tgb}{tga*tgb+1}$

In cazul de fata, $a=\frac{7\pi}{12}$ si $b=\frac{5\pi}{12}$.

Aplicam formula de mai sus:

$\frac{tg\frac{7\pi}{12}-tg\frac{5\pi}{12}}{tg\frac{7\pi}{12}*tg\frac{5\pi}{12}+1}=tg(\frac{7\pi}{12}-\frac{5\pi}{12})=tg(\frac{2\pi}{12})=tg(\frac{\pi}{6})=\frac{\sqrt3}{3}$