Question

Вычеслите:ctg(arccos (-1/2))
ctg(3 arccos(-1) + arcsin(-1/2))

Answer 1

$ctg\left(\arccos\left(-\dfrac{1}{2}\right)\right) = ctg\left(\dfrac{2\pi}{3}\right) = \boxed{\bf{-\dfrac{\sqrt{3}}{3}}}$

$ctg\left(3\arccos(-1) + \arcsin\left(-\dfrac{1}{2}\right)\right) = ctg\left(3\pi + \left(-\dfrac{\pi}{6}\right)\right) = ctg\left(3\pi - \dfrac{\pi}{6}\right)=\\\\\\= ctg\left(-\dfrac{\pi}{6}\right) = -ctg\dfrac{\pi}{6} = \boxed{\bf{-\sqrt{3}}}$