Question

Assinale a alternativa que indica, aproximadamente, a tg pi/3 + tg 5 pi/6 . tg 7 pi/4.

Considere V3 = 1.7.
(A) 1,27
(B) 1,64.
(C) 1.86.
(D) 2.28.
(E) 2,73​

Answer 1

Explicação passo-a-passo:

$\sf tg~\left(\dfrac{\pi}{3}\right)+tg~\left(\dfrac{5\pi}{3}\right)\cdot tg~\left(\dfrac{7\pi}{4}\right)$

$\sf =\sqrt{3}+\left[-\dfrac{\sqrt{3}}{3}\cdot(-1)\right]$

$\sf =\sqrt{3}+\dfrac{\sqrt{3}}{3}$

$\sf =1,7+\dfrac{1,7}{3}$

$\sf =1,7+0,57$

$\sf =2,28$ aproximadamente

Letra D