Question

Exercițiul 53, va rog.

Answer 1

Răspuns:

Explicație pas cu pas:

$tg\left(x+\dfrac{\pi}{3}\right)=\dfrac{tg~x+tg\frac{\pi}{3}}{1-tg~x\cdot tg\frac{\pi}{3}}=\dfrac{\frac{1}{2}+\sqrt 3}{1-\frac{1}{2}\cdot \sqrt 3}=\dfrac{1+2\sqrt 3}{2-\sqrt 3}=\dfrac{(1+2\sqrt 3)(2+\sqrt 3)}{4-3}\\=(1+2\sqrt 3)(2+\sqrt 3)=2+\sqrt 3+4\sqrt 3+2\cdot 3=\boxed{8+4\sqrt 3}$