Question

y= cotg$\frac{5 \pi }{3}$-Tg$\frac{pi }{6}$

Answer 1

Veja que:
$cotg\alpha=\frac{1}{tg\alpha}$

Dessa forma teremos:
$cotg \frac{5\pi}{3} = \frac{1}{tg\frac{5\pi}{3}}$

Só que:
$tg\frac{5\pi}{3}=tg(2\pi-\frac{\pi}{3})=-tg\frac{\pi}{3}=-\sqrt{3}$

Logo, $cotg\frac{5\pi}{3}=\frac{-1}{\sqrt{3}}=\frac{-\sqrt{3}}{3}$

Além disso, $tg\frac{pi}{6}=\frac{\sqrt{3}}{3}$

Com isso teremos:
$Y = \frac{-\sqrt{3}}{3} . \frac{\sqrt{3}}{3} = -\frac{1}{3}$